##
REAL BANACH ALGEBRAS AS *𝒞* (*𝒦*) ALGEBRAS

in** The Quarterly Journal of Mathematics**

September 2012; p ublished online April 2011 .

Journal Article. Subjects: Pure Mathematics. 0 words.

The classical theorem of Gelfand provides a representation of a commutative complex unital Banach algebra as a subalgebra of *𝒞*
_{ℂ}(*𝒦*) of continuous complex-valued functions...

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## On Bernstein Type and Maximal Inequalities for Dependent Banach-Valued Random Vectors and Applications

in** The Oxford Handbook of Functional Data Analysis**

November 2010; p ublished online August 2018 .

Article. Subjects: Mathematics. 22490 words.

This article discusses some results on Bernstein type and maximal inequalities for partial sums of dependent random vectors taking their values in separable Hilbert or Banach spaces of...

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** » ** abstract

## The Structure of Triple Derivations on Semisimple Banach *-Algebras

in** The Quarterly Journal of Mathematics**

September 2017; p ublished online February 2017 .

Journal Article. Subjects: Pure Mathematics. 7725 words.

**Abstract**

Triple derivations on *C*
^{*}-algebras and JB^{*}-triples had been extensively studied in the literature. In this paper, we characterize the...

## Stability of abstract non-linear non-autonomous difference-delay equations

in** IMA Journal of Mathematical Control and Information**

June 2009; p ublished online June 2009 .

Journal Article. Subjects: Mathematics. 0 words.

We consider a class of functional–difference equations in a Banach space with causal operators, which have the local Lipschitz property. Sufficient conditions for the boundedness of...

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## From linear to nonlinear equations, fundamental results

in** Numerical Methods for Nonlinear Elliptic Differential Equations**

October 2010; p ublished online January 2011 .

Chapter. Subjects: Mathematical and Statistical Physics. 8208 words.

Chapter 1 demonstrates, for the simple mechanical example of a bent rod, the change in character from linear to nonlinear regimes. This is followed by several examples for different types...

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## BOUNDARIES FOR STRONG SCHUR SPACES

in** The Quarterly Journal of Mathematics**

September 2014; p ublished online August 2013 .

Journal Article. Subjects: Pure Mathematics. 0 words.

It is known that if a Banach space *X* does not contain an isomorphic copy of *c*
_{0}, then for any boundary *B* and representation *B* = ∪^{∞}
_{
n=1}
*B*null...

## Geometric interpolation of entropy numbers

in** The Quarterly Journal of Mathematics**

June 2018; p ublished online September 2017 .

Journal Article. Subjects: Pure Mathematics. 7661 words.

**Abstract**

We investigate whether the entropy numbers of an operator behave well under the complex interpolation between Hilbert spaces. We study geometric...

## Disentangling: Definitions, Properties and Elementary Examples

in** Feynman's Operational Calculus and Beyond**

August 2015; p ublished online September 2015 .

Chapter. Subjects: Mathematical and Statistical Physics; Mathematics. 20736 words.

A rigorous approach to Feynman’s operational calculus, the formation of functions of several noncommuting operators, is introduced, using Feynman’s heuristic “rules” as a guide. Two...

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## Fr ´Echet Differentiability of Vector-Valued Functions

in** Fréchet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces (AM-179)**

February 2012; p ublished online October 2017 .

Chapter. Subjects: Mathematics. 15173 words.

This chapter shows that if a Banach space with a Fréchet smooth norm is asymptotically smooth with modulus *o*(*t*ⁿ logⁿ⁻¹(1/*t*)) then every Lipschitz map of *X* to a space of dimension not...

## A modification of the Chebyshev method

in** IMA Journal of Numerical Analysis**

October 1997; p ublished online October 1997 .

Journal Article. Subjects: Mathematics. 0 words.

In this paper we use a one-parametric family of second-order iterations to solve a nonlinear operator equation in a Banach space. Two different analyses of convergence are shown. First,...

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## When absolute continuity on C‐algebras is automatically uniform

in** The Quarterly Journal of Mathematics**

March 2004; p ublished online March 2004 .

Journal Article. Subjects: Pure Mathematics. 0 words.

Let *A* be a C^{*}‐algebra and let *K* be a relatively weakly compact subset of the dual of *A*. Let ψbe a positive linear functional on *A* such that, for each φin *K*, φis strongly absolutely...

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** » ** abstract

## NON-COMMUTATIVE LOCALLY CONVEX MEASURES

in** The Quarterly Journal of Mathematics**

March 2011; p ublished online June 2009 .

Journal Article. Subjects: Pure Mathematics. 0 words.

We study weakly compact operators from a *C**-algebra with values in a complete locally convex space. They constitute a natural non-commutative generalization of finitely additive vector...

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## Fr ´Echet Differentiability Except For Γ-Null Sets

in** Fréchet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces (AM-179)**

February 2012; p ublished online October 2017 .

Chapter. Subjects: Mathematics. 7151 words.

This chapter gives an account of the known genuinely infinite dimensional results proving Fréchet differentiability almost everywhere except for Γ-null sets. Γ-null sets provide the only...

##
*Ε*-Fr ´Echet Differentiability

in** Fréchet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces (AM-179)**

February 2012; p ublished online October 2017 .

Chapter. Subjects: Mathematics. 9636 words.

This chapter treats results on ε-Fréchet differentiability of Lipschitz functions in asymptotically smooth spaces. These results are highly exceptional in the sense that they prove almost...

##
BAIRE CLASSES OF NON-SEPARABLE *L*
_{1}-PREDUALS

in** The Quarterly Journal of Mathematics**

March 2015; p ublished online June 2014 .

Journal Article. Subjects: Pure Mathematics. 0 words.

Let *X* be an *L*
_{1}-predual, non-separable in general. We show that the intrinsic Baire classes of *X* can be identified with the spaces of odd Baire functions on the set ext *B*null...

## Disentangling via Tensor Products and Ordered Supports

in** Feynman's Operational Calculus and Beyond**

August 2015; p ublished online September 2015 .

Chapter. Subjects: Mathematical and Statistical Physics; Mathematics. 20732 words.

More involved types of disentanglings are considered in this chapter. We discuss the situation where the Banach space *X* can be written as a direct sum X=Y⊕Z, for some Banach spaces *Y* and Z,...

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## A parallel method for time discretization of parabolic equations based on Laplace transformation and quadrature

in** IMA Journal of Numerical Analysis**

April 2003; p ublished online April 2003 .

Journal Article. Subjects: Mathematics. 0 words.

We consider the discretization in time of an inhomogeneous parabolic equation in a Banach space setting, using a representation of the solution as an integral along a smooth curve in the...

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## LINEAR CAUCHY PROBLEM WITH VARIABLE COEFFICIENTS

in** Multi-dimensional hyperbolic partial differential equations**

November 2006; p ublished online September 2007 .

Chapter. Subjects: Applied Mathematics. 17084 words.

This chapter emphasizes energy estimates, that is, *a priori* estimates without loss of derivatives in Sobolev spaces. The appropriate tools are functional symmetrizers, obtained merely as...

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## Basic Principles of Linear Analysis

in** Real Analysis**

October 2016; p ublished online January 2017 .

Chapter. Subjects: Mathematics. 30959 words.

This chapter on the basic principles of linear analysis presents elements of functional analysis that are frequently used in setting up spaces on which certain operators intimately related...

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## COMPLETENESS OF *-SYMMETRIC GELFAND–NAIMARK–SEGAL INNER PRODUCT SPACES

in** The Quarterly Journal of Mathematics**

June 2012; p ublished online June 2012 .

Journal Article. Subjects: Pure Mathematics. 0 words.

Every state *ϱ* on a *C**-algebra *A* induces a *-symmetric semi-inner product (*x*, *y*)↦ *ϱ*(*y** *x*) + *ϱ*(*xy**) (*x*, *y* ∈ *A*). The main scope of the paper is to characterize those states for which the...

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