##
*H*
^{∞} Functional Calculus and Maximal Inequalities for Semigroups of Contractions on Vector-Valued *L*
_{
p
}-Spaces

in** International Mathematics Research Notices**

January 2015; p ublished online July 2014 .

Journal Article. Subjects: Mathematics. 4509 words.

Let {*T*
_{
t
}}_{
t>0} be a strongly continuous semigroup of positive contractions on *L*
_{
p
}(*X*,*μ*) with...

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** » ** abstract

## Optimal control for linear discrete-time systems with Markov perturbations in Hilbert spaces

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

March 2009; p ublished online March 2009 .

Journal Article. Subjects: Mathematics. 0 words.

In this article, we discuss a quadratic control problem for linear discrete-time systems with Markov perturbations in Hilbert spaces, which is linked to a discrete-time Riccati equation...

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** » ** abstract

## Oscillations in lossless propagation models: a Liapunov–Krasovskii approach

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

March 2002; p ublished online March 2002 .

Journal Article. Subjects: Mathematics. 0 words.

This paper focuses on Forced oscillations (periodic and almost periodic) in some dynamical models described by coupled differential and difference equations. The existence and stability...

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** » ** abstract

## Essential Spectra

in** Spectral Theory and Differential Operators**

May 2018; p ublished online September 2018 .

Chapter. Subjects: Pure Mathematics. 27584 words.

In this chapter, various essential spectra are studied. For a closed operator in a Banach space, a number of different sets have been used for the essential spectrum, the sets being...

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** » ** abstract

## ASYMPTOTIC UNCONDITIONALITY

in** The Quarterly Journal of Mathematics**

June 2010; p ublished online January 2009 .

Journal Article. Subjects: Pure Mathematics. 0 words.

We show that a separable real Banach space embeds almost isometrically in a space *Y* with a shrinking 1-unconditional basis if and only if lim _{
n→∞}‖ *x** + *x*
_{null...}

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** » ** abstract

##
ISOMETRIES BETWEEN SPACES OF REAL POLYNOMIALS OF DEGREE AT MOST *n*

in** The Quarterly Journal of Mathematics**

June 2016; p ublished online March 2016 .

Journal Article. Subjects: Pure Mathematics. 8072 words.

Given real Banach spaces [math] and [math], we show that every isometric isomorphism from the space of approximable polynomials of degree at most [math] on [math] to the space of...

## Spectral Theory for Noncommuting Operators

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

August 2015; p ublished online September 2015 .

Chapter. Subjects: Mathematical and Statistical Physics; Mathematics. 9320 words.

This chapter, on spectral theory for noncommuting operators, seeks to extend the operational calculus beyond the setting of the analytic functions in the disentangling algebra. When the...

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** » ** abstract

## Gâteaux differentiability of Lipschitz 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. 4791 words.

This chapter presents the main results on Gâteaux differentiability of Lipschitz functions by recalling the notions of the Radon-Nikodým property (RNP) and null sets. The discussion focuses...

## BROWNIAN ROUGH PATHS

in** System Control and Rough Paths**

December 2002; p ublished online September 2007 .

Chapter. Subjects: Probability and Statistics. 30047 words.

This chapter proves that the dyadic polygonal approximations to a Brownian paths, with probability 1, a Cauchy sequence of rough paths, and in this way, the chapter proves a result first...

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** » ** abstract

## THE PME AS AN ABSTRACT EVOLUTION EQUATION. SEMIGROUP APPROACH

in** The Porous Medium Equation**

October 2006; p ublished online September 2007 .

Chapter. Subjects: Mathematical and Statistical Physics. 14319 words.

This chapter addresses the problem of the construction of solutions of the GPME by viewing it as an abstract evolution equation, or more precisely as an ordinary differential equation with...

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** » ** abstract

## Operator Algebras and Their Modules

October 2004; p ublished online September 2007 .

Book. Subjects: Pure Mathematics. 398 pages.

This book presents the general theory of algebras of operators on a Hilbert space, and the modules over such algebras. The new theory of operator spaces is presented early on and the text...

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** » ** abstract

##
Γ-Null and Γ*N*-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. 10215 words.

This chapter introduces the notions of Γ-null and Γₙ-null sets, which are σ-ideals of subsets of a Banach space *X*. Γ-null set is key for the strongest known general Fréchet...

## Set convergence for discretizations of the attractor

in** IMA Journal of Numerical Analysis**

April 1996 .

Journal Article. Subjects: Mathematics. 0 words.

We consider the discretization of a dynamical system given by a *C*
^{0}-semigroup *S*(*t*), defined on a Banach space *X*, possessing an attractor 𝒜. Under certain weak assumptions,...

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** » ** abstract

## Kolmogorov widths under holomorphic mappings

in** IMA Journal of Numerical Analysis**

January 2016; p ublished online March 2015 .

Journal Article. Subjects: Mathematics; Numerical and Computational Mathematics. 4227 words.

If [math] is a bounded linear operator mapping the Banach space [math] into the Banach space [math] and [math] is a compact set in [math], then the Kolmogorov widths of the image [math] do...

## On controllability of second-order impulsive neutral integrodifferential systems with infinite delay

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

September 2015; p ublished online April 2014 .

Journal Article. Subjects: Mathematics. 0 words.

This article is concerned with the controllability of damped second-order impulsive neutral integrodifferential systems with infinite delay in Banach spaces. A set of sufficient conditions...

## An infinite-dimensional manifold structure for analytic Lie pseudogroups of infinite type

in** International Mathematics Research Notices**

January 2004; p ublished online January 2004 .

Journal Article. Subjects: Mathematics. 0 words.

We construct an infinite-dimensional manifold structure adapted to analytic Lie pseudogroups of infinite type. More precisely, we prove that any isotropy subgroup of an analytic Lie...

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** » ** abstract

##
On coarse embeddings into *c*
_{0}(Γ)

in** The Quarterly Journal of Mathematics**

March 2018; p ublished online August 2017 .

Journal Article. Subjects: Pure Mathematics. 3299 words.

**Abstract**

Let λ be a large enough cardinal number (assuming the Generalized Continuum Hypothesis it suffices to let [math]). If *X* is a Banach space with [math],...

## Unavoidable Porous Sets and Nondifferentiable Maps

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

February 2012; p ublished online October 2017 .

Chapter. Subjects: Mathematics. 12622 words.

This chapter discusses Γₙ-nullness of sets porous “¹at infinity” and/or existence of many points of Fréchet differentiability of Lipschitz maps into *n*-dimensional spaces. The results...

##
Preduals of JBW^{*}-triples are 1-Plichko spaces

in** The Quarterly Journal of Mathematics**

June 2018; p ublished online December 2017 .

Journal Article. Subjects: Pure Mathematics. 17763 words.

**Abstract**

We investigate the preduals of JBW^{*}-triples from the point of view of Banach space theory. We show that the algebraic structure of a JBW^{*}-triple *M* nat...

## Lp Spaces

in** Real Analysis**

October 2016; p ublished online January 2017 .

Chapter. Subjects: Mathematics. 22966 words.

L^{
P
} spaces are the most interesting examples of Banach spaces and play a salient role in modern analysis. In this chapter, basic features of L^{
Pnull...}

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