The Johnson-Lindenstrauss lemma almost characterizes Hilbert space, but not quite (2009)
William B. Johnson, Assaf Naor
Let X be a normed space that satisfies the Johnson-Lindenstrauss lemma (J-L lemma, in short) in the sense that for any integer n and any x1,..., xn ∈ X there exists a linear mapping L: X → F,...
Lipschitz p-summing Operators ∗ (2009)
Jeffrey D. Farmer, William B. Johnson
The notion of Lipschitz p-summing operator is introduced. A non linear Pietsch factorization theorem is proved for such operators and it is shown that a Lipschitz p-summing operator that is linear is...
William B. Johnson, Bernard Maurey, Gideon Schechtman
factorization of linear operators ∗
The Johnson-Lindenstrauss lemma almost characterizes Hilbert space, but not quite (2009)
William B. Johnson, Assaf Naor
Let X be a normed space that satisfies the Johnson-Lindenstrauss lemma (J-L lemma, in short) in the sense that for any integer n and any x1,..., xn ∈ X there exists a linear mapping L: X → F,...
Commutators on $\ell_{\infty}$ (2009)
Dosev, Detelin, Johnson, William B.
The operators on $\ell_{\infty}$ which are commutators are those not of the form $\lambda I + S$ with $\lambda\neq 0$ and $S$ strictly singular.
The Johnson-Lindenstrauss lemma almost characterizes Hilbert space, but not quite (2008)
Johnson, William B., Naor, Assaf
Let $X$ be a normed space that satisfies the Johnson-Lindenstrauss lemma (J-L lemma, in short) in the sense that for any integer $n$ and any $x_1,\ldots,x_n\in X$ there exists a linear mapping...
William B. Johnson, Bernard Maurey, Gideon Schechtman
factorization of linear operators ∗
Finite dimensional subspaces of L p (2007)
William B. Johnson, Gideon Schechtman
We discuss the finite dimensional structure theory of L p; in particular, the theory of restricted invertibility and classification of subspaces of # n p. Contents 1
The "Full Müntz Theorem" in L_p[0,1] for . . . (2007)
Tamás Erdélyi, William B. Johnson
. Denote by span{f1 , f2 , . . . } the collection of all finite linear combinations of the functions f1 , f2 , . . . over R. The principal result of the paper is the following. Theorem (Full Muntz...
the collection of all finite linear combinations of the functions f1, f2,... over R. The principal result of the paper is the following. Theorem (Full Muntz Theorem in Lp (A) for p
William B. Johnson, Joram Lindenstrauss, David Preiss, Gideon Schechtman
mappings between infinite dimensional Banach spaces
POWER TYPE UNIFORM CONVEXITY OF X VIA p-ASYMPTOTIC UNIFORM CONVEXITY OF L r (X) (2007)
C Esar, L. Garc, William B. Johnson, Communicated Gilles Pisier
Abstract. We show that if Lr (X), 1 has an asymptotically uniformly convex renorming of power type then X admits a uniformly convex norm of power type. 1.
William B. Johnson, Timur Oikhberg, Gamma P, Gamma P
Abstract. A Banach space X is said to have the separable lifting property if for every subspace Y of X # # containing X and such that Y/X is separable there exists a bounded linear lifting from Y/X...
Very tight embeddings of subspaces of L p, 1 p 2, into n (2007)
William B. Johnson, Gideon Schechtman
We prove that for 1 p < r < 2, every n-dimensional subspace E of L r , in particular ` r , well-embeds into ` p for some m (1 + )n, where \well" depends on p, r, and the arbitrary > 0,...
The "Full Müntz Theorem" in L_p[0, 1] for 0 < p < ∞ (2007)
Tamas Erdelyi, William B. Johnson
this paper is the following. positive lower density at 0.Letp#(0,#).Suppose(# j ) # j=1 is a sequence of distinct real =#
Multiplication operators on L(L_p) and $\ell_p$-strictly singular operators (2007)
Johnson, William B., Schechtman, Gideon
A classification of weakly compact multiplication operators on L(L_p), $1
Operators into Lp which Factor Through lp (2006)
A bounded linear operator T into Lp[0, 1] (2 < p < ∞ ) factors through lp if and only if T is compact when considered as an operator into L2[0, 1].
Human Decision-Making in Computer Aided Fault Diagnosis. (2002)
Rouse,William B., Rouse,Sandra H., Hunt,Ruston M., Johnson,William B., Pelligrino,Susan J.
This report summarizes a series of six experiments conducted to increase our understanding of human performance on diagnostic tasks, and in the process to investigate the feasibility of using...
An Annotated Selective Bibliography on Human Performance in Fault Diagnosis Tasks. (2002)
Johnson,William B., Rouse,Sandra H., Rouse,William B.
This is an annotated bibliography of 61 published works about human performance in fault diagnosis. The sources are predominately from the disciplines of engineering, psychology, and education....
Johnson,William B., Entwistle,William C., Gaddis,Karen S.
In 1979 the University of Illinois developed a computer-based simulation designed to assist aviation maintenance trainees in acquiring troubleshooting skills. This simulation was named FAULT...
Lipschitz quotients from metric trees and from Banach spaces containing l1 (2002)
William B. Johnson, Joram Lindenstrauss, David Preiss, Gideon Schechtman
containing ` 1
Lipschitz quotients from metric trees and from Banach spaces containing l1 (2002)
William B. Johnson, Joram Lindenstrauss, David Preiss, Gideon Schechtman
A Lipschitz map f between the metric spaces X and Y is called a Lipschitz quotient map if there is a C> 0 (the smallest such C, the co-Lipschitz constant, is denoted coLip(f), while Lip(f) denotes
William B. Johnson, Joram Lindenstrauss, David Preiss, Gideon Schechtman
We give several sufficient conditions on a pair of Banach spaces X and Y under which each Lipschitz mapping from a domain in X to Y has, for every #> 0, a point of #-Frechet differentiability....
Human Factors in Aviation Maintenance. Phase 1 (2000)
Shepherd, William T., Johnson, William B., Druray, Colin G., Taylor, James C., Berninger, Daniel
This human factors research in aviation maintenance addresses four tasks including studies of organizational behaviour, job and task analysis in maintenance and inspection, advanced technology for...
Separable Lifting Property And Extensions Of Local Reflexivity (2000)
William B. Johnson, Timur Oikhberg, Gamma P, Gamma P
. A Banach space X is said to have the separable lifting property if for every subspace Y of X ## containing X and such that Y/X is separable there exists a bounded linear lifting from Y/X to Y . We...
William B. Johnson, Joram Lindenstrauss, David Preiss, Gideon Schechtman
We give several sufficient conditions on a pair of Banach spaces X and Y under which each Lipschitz mapping from a domain in X to Y has, for every ffl ? 0, a point of ffl-Fr'echet...
TROOP POSTURE SEQUENCES FOR DISMOUNTED ARMORED INFANTRYMEN. (1998)
Gschwind,Robert T., Nair,Ward M., Johnson,William B.
This field experiment measured the posture sequence of armored infantrymen taking cover under and inside armored personnel carriers. Additionally, probability functions were developed for the exposed...
Development and Demonstration of Microcomputer Intelligence for Technical Training (MITT). (1998)
Johnson, William B., Hunt, Ruston M., Duncan, Phillip C., Norton, Jeffrey E.
The Microcomputer Intelligence for Technical Training research described here is founded upon a proven intelligent diagnostic training simulation to construct enhanced models of the student,...
Initial Evaluation of Principles for Graphical Displays in Maintenance Problem Solving. (1998)
Sewell, Daniel R., Rouse, William B., Johnson, William B.
This paper reports the findings of two studies of the use of diagrams for maintenance problem solving. One study involved a protocol analysis of one maintainer working three maintenance problems. The...
Computational Approaches for Analyzing Tradeoffs Between Training and Aiding. (1998)
Rouse, William B., Johnson, William B.
This paper presents a methodological framework for representing tradeoffs among alternative combinations of training and aiding for personnel in complex systems. A wide variety of methods, tools, and...
A Review of New Training Technology at the U.S. Army Signal School. (1998)
Johnson, William B., Sanders, Michael G.
The Signal School and the U.S. Army Research Institute for the Behavioral and Social Sciences (ARI) Fort Gordon field Unit surveyed and assessed training technology both within and outside of the...
Wiederholt, Bradley J., Norton, Jeffrey E., Johnson, William B., Browning, Elica J.
MITT Writer is a software system for development of computer based training for complex technical domains. MITT Writer allows a student to learn and practice troubleshooting and diagnostic skills....
Diamond/Al Metal Matrix Composites Formed by the Pressureless Metal Infiltration Process. (1998)
Johnson, William B., Sonuparlak, B.
Diamond particles are unique fillers for metal matrix composites because of their extremely high modulus, high thermal conductivity, and low coefficient of thermal expansion. diamond reinforced...
Reinforced Si3N4 Matrix Composites Formed by the Directed Metal Oxidation Process. (1998)
Silicon nitride has many desirable characteristics for ceramic structural applications in heat engines. It has high room temperature strength, high retained strength at temperatures up to 1300 C,...
Breval, Else, Johnson, William B.
The microstructure of a ZrB2-platelet-reinforced ZrC(x) composite was examined using transmission electron microscopy and X-ray diffraction. The composites, which are formed by the reaction of molten...
Johnson, William B., Nagelberg, Alan S., Breval, Else
The kinetics of formation of a new class of ceramic composite material, zirconium diboride platelet-reinforced zirconium carbides, are discussed. These materials are prepared by the directed reaction...
Johnson, William B., Nagelberg, Alan S., Breval, Else
The kinetics of formation of a new class of ceramic composite material, zirconium diboride platelet-reinforced zirconium carbides, are discussed. These materials are prepared by the directed reaction...
Bates, Sean M., Johnson, William B., Lindenstrauss, Joram, Preiss, D., Schechtman, Gideon
New concepts related to approximating a Lipschitz function between Banach spaces by affine functions are introduced. Results which clarify when such approximations are possible are proved and in some...
Banach spaces determined by their uniform structures (1997)
Johnson, William B., Lindenstrauss, Joram, Schechtman, Gideon
Following results of Bourgain and Gorelik we show that the spaces $\ell_p$, $1
If $X$ is a closed subspace of a Banach space $L$ which embeds into a Banach lattice not containing $\ell_\infty^n$'s uniformly and $L/X$ contains $\ell_\infty^n$'s uniformly, then $X$ cannot have...
Banach Spaces Determined By Their Uniform Structures (1996)
William B. Johnson, Joram Lindenstrauss, Gideon Schechtman
Following results of Bourgain and Gorelik we show that the spaces ` p , 1 ! p ! 1, as well as some related spaces have the following uniqueness property: If X is a Banach space uniformly homeomorphic...
Universal Non-Completely-Continuous Operators (1995)
Girardi, Maria, Johnson, William B.
A bounded linear operator between Banach spaces is called {\it completely continuous} if it carries weakly convergent sequences into norm convergent sequences. Isolated is a universal operator for...
Almost Frechet differentiability of Lipschitz maps between infinite dimensional Banach spaces (1995)
William B. Johnson, Joram Lindenstrauss, David Preiss, Gideon Schechtman
We give several sufficient conditions on a pair of Banach spaces X and Y under which each Lipschitz mapping from a domain in X to Y has, for every #> 0, a point of #-Frechet di#erentiability. Most...
The Complete Continuity Property And Finite Dimensional Decompositions (1995)
Maria Girardi, William B. Johnson
. A Banach space X has the complete continuity property (CCP) if each bounded linear operator from L1 into X is completely continuous (i.e., maps weakly convergent sequences to norm convergent...
Extension of Operators from Weak$^*$-closed Subspaces of $\ell_1$ (1994)
Johnson, William B., Zippin, M.
It is proved that every operator from a weak$^*$-closed subspace of $\ell_1$ into a space $C(K)$ of continuous functions on a compact Hausdorff space $K$ can be extended to an operator from $\ell_1$...
Banach spaces with the $2$-summing property (1994)
Arias, Alvaro, Figiel, Tadek, Johnson, William B., Schechtman, Gideon
A Banach space $X$ has the $2$-summing property if the norm of every linear operator from $X$ to a Hilbert space is equal to the $2$-summing norm of the operator. Up to a point, the theory of spaces...
The Complete Continuity Property and Finite Dimensional Decompositions (1993)
Girardi, Maria, Johnson, William B.
A Banach space $\X$ has the complete continuity property (CCP) if each bounded linear operator from $L_1$ into $\X$ is completely continuous (i.e., maps weakly convergent sequences to norm convergent...
Bochner vs. Pettis norm: examples and results (1993)
S. J. Dilworth, Maria Girardi, Banach Spaces, Bor-luh Lin, William B. Johnson
. Our basic example shows that for an arbitrary infinite-dimensional Banach space X, the Bochner norm and the Pettis norm on L 1 (X) are not equivalent. Refinements of this example are then used to...
Polynomial Schur and Polynomial Dunford-Pettis Properties (1992)
Farmer, Jeff, Johnson, William B.
A Banach space is {\it polynomially Schur} if sequential convergence against analytic polynomials implies norm convergence. Carne, Cole and Gamelin show that a space has this property and the...
Computing p-summing norms with few vectors (1992)
Johnson, William B., Schechtman, Gideon
It is shown that the p-summing norm of any operator with n-dimensional domain can be well-aproximated using only ``few" vectors in the definition of the p-summing norm. Except for constants...
Factorizations of natural embeddings of l_p^n int L_r (1992)
Figiel, Tadek, Johnson, William B., Schechtman, Gideon
This is a continuation of the paper [FJS] with a similar title. Several results from there are strengthened, in particular: 1. If T is a "natural" embedding of l_2^n into L_1 then, for any...
Analytic Disks in Fibers over the Unit Ball of a Banach Space (1991)
Cole, B. J., Gamelin, T. W., Johnson, William B.
We study biorthogonal sequences with special properties, such as weak or weak-star convergence to 0, and obtain an extension of the Josefson-Nissenzweig theorem. This result is applied to embed...
Space Station Training Office (1991)
Bradley J. Wiederholt, Elica J. Browning, Jeffrey E. Norton, William B. Johnson
F- j " t:..... yt _-j
The proportional UAP characterizes weak Hilbert spaces (1990)
Johnson, William B., Pisier, Gilles
We prove that a Banach space has the uniform approximation property with proportional growth of the uniformity function iff it is a weak Hilbert space.
Operators which factor through Banach lattices not containing c_0 (1990)
Ghoussoub, Nassif, Johnson, William B.
In this supplement to [GJ1], [GJ3], we give an intrinsic characterization of (bounded, linear) operators on Banach lattices which factor through Banach lattices not containing a copy of $c_0$ which...
Remarks on Talagrand's deviation inequality for Rademacher functions (1990)
Johnson, William B., Schechtman, Gideon
Recently Talagrand [T] estimated the deviation of a function on $\{0,1\}^n$ from its median in terms of the Lipschitz constant of a convex extension of $f$ to $\ell ^n_2$; namely, he proved that...
Characterization of hydrogenated, amorphous carbon thin films / (1988)
Thesis (M.S.)--Ohio State University, 1988.
Advisor: William B. Johnson, Dept. of Metallurgical Engineering.
Advisor: William B. Johnson, Dept. of Metallurgical Engineering; Co-Advisor: George R. St. Pierre, Dept. of Metallurgical Engineering.
Contemporary Mathematics (1984)
William B. Johnson, Gideon Schechtman
We discuss the finite dimensional structure theory of L p; in particular, the theory of restricted invertibility and classification of subspaces of ` n p. Contents 1
Symmetric structures in Banach spaces / W. B. Johnson ... [et al.] (1979)
Incluye bibliografía
Finite dimensional subspaces of L_p
William B. Johnson, Gideon Schechtman
this article, we chose to devote this section to describing the change of densities that arise later. It turns out that the framework in which this technique is most naturally used is that of an L p...