## Borel–Weil Theory for Root Graded Banach–Lie Groups

in** International Mathematics Research Notices**

January 2010; p ublished online October 2009 .

Journal Article. Subjects: Mathematics. 11165 words.

In this article, we introduce (weakly) root graded Banach–Lie algebras and corresponding Lie groups as natural generalizations of group like
for a Banach algebra *A* or groups like *C*(*X*,*K*)...

## THE SPECTRUM OF VOLTERRA OPERATORS ON WEIGHTED SPACES OF ENTIRE FUNCTIONS

in** The Quarterly Journal of Mathematics**

September 2015; p ublished online June 2015 .

Journal Article. Subjects: Pure Mathematics. 4544 words.

We investigate the spectrum of the Volterra operator [math] with symbol an entire function [math], when it acts on weighted Banach spaces [math] of entire functions with sup-norms and when...

## Numerical‐Radius‐Attaining Polynomials

in** The Quarterly Journal of Mathematics**

March 2003; p ublished online March 2003 .

Journal Article. Subjects: Pure Mathematics. 0 words.

In this paper we discuss a version of James theorem making use of polynomials which attain their numerical radius. In addition, we obtain a characterization of finite‐dimensional Banach...

##
On the dentability of weak*-*H*_{δ}
sets

_{δ}

in** The Quarterly Journal of Mathematics**

September 2005; p ublished online September 2005 .

Journal Article. Subjects: Pure Mathematics. 0 words.

We state several conditions equivalent to weak^{*}-dentability for certain subsets of a dual Banach space which include both the compact case and a result of Ghoussoub and Maurey.

## DUALITY IN SPACES OF LORCH ANALYTIC MAPPINGS

in** The Quarterly Journal of Mathematics**

September 2016; p ublished online September 2016 .

Journal Article. Subjects: Pure Mathematics. 4433 words.

For a complex Banach algebra [math], we study the strong dual of the Fréchet space [math] of the mappings [math] that are analytic in the sense of Lorch. First, we will show that [math] is...

## POLYNOMIAL NUMERICAL INDEX FOR SOME COMPLEX VECTOR-VALUED FUNCTION SPACES

in** The Quarterly Journal of Mathematics**

December 2008; p ublished online January 2008 .

Journal Article. Subjects: Pure Mathematics. 0 words.

We study the relation between the polynomial numerical indices of a complex vector-valued function space and the ones of its range space. It is proved that the spaces *C*(*K*, *X*) and *L*null...

## SEMISIMPLE BANACH ALGEBRAS GENERATED BY STRONGLY CONTINUOUS REPRESENTATIONS OF MOORE GROUPS

in** The Quarterly Journal of Mathematics**

June 2008; p ublished online December 2007 .

Journal Article. Subjects: Pure Mathematics. 0 words.

We prove that if τ is a strongly continuous bounded representation of a Moore group *G* on a Banach space *X*, and if the Arveson spectrum of τ is scattered, then the closure with respect to...

## Smoothness, Convexity, Porosity, and Separable Determination

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

February 2012; p ublished online October 2017 .

Chapter. Subjects: Mathematics. 8604 words.

This chapter shows how spaces with separable dual admit a Fréchet smooth norm. It first considers a criterion of the differentiability of continuous convex functions on Banach spaces before...

##
A NOTE ON FRAGMENTABILITY AND WEAK-*G*
_{
δ
} SETS

in** The Quarterly Journal of Mathematics**

June 2012; p ublished online June 2012 .

Journal Article. Subjects: Pure Mathematics. 0 words.

In terms of fragmentability, we describe a new class of Banach spaces which may be *c*
_{0}-saturated but do not contain weak-*G*
_{
δ
} open...

## The vector-valued nonhomogeneous Tb Theorem

in** International Mathematics Research Notices**

January 2014; p ublished online October 2012 .

Journal Article. Subjects: Mathematics. 12407 words.

This paper gives a Banach space-valued extension of the Tb theorem of Nazarov et al. [20] concerning the boundedness of singular integral operators with respect to a measure *μ*, which only...

## UNIQUENESS OF THE EXTENSION OF 2-HOMOGENEOUS POLYNOMIALS

in** The Quarterly Journal of Mathematics**

December 2010; p ublished online April 2009 .

Journal Article. Subjects: Pure Mathematics. 0 words.

Homogeneous polynomials of degree 2 on the complex Banach space *c*
_{0}(ℓ_{
n
}
^{2}) are shown to have unique norm-preserving extension to the...

## COARSE AND UNIFORM EMBEDDINGS INTO REFLEXIVE SPACES

in** The Quarterly Journal of Mathematics**

September 2007; p ublished online June 2007 .

Journal Article. Subjects: Pure Mathematics. 0 words.

**Abstract**

Answering an old problem in nonlinear theory, we show that *c*
_{0} cannot be coarsely or uniformly embedded into a reflexive Banach space,...

##
PROJECTIVITY OF BANACH AND *C**-ALGEBRAS OF CONTINUOUS FIELDS

in** The Quarterly Journal of Mathematics**

June 2013; p ublished online March 2012 .

Journal Article. Subjects: Pure Mathematics. 0 words.

We give necessary and sufficient conditions for the left projectivity and biprojectivity of Banach algebras defined by locally trivial continuous fields of Banach algebras. We identify...

## Non-linear fractional integro-differential systems with non-local conditions

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

June 2016; p ublished online November 2014 .

Journal Article. Subjects: Mathematics. 4251 words.

We prove the existence of mild solutions of fractional integro-differential equations with non-local conditions in Banach spaces. Sufficient conditions for controllability of fractional...

## Operator splitting for abstract Cauchy problems

in** IMA Journal of Numerical Analysis**

July 1998; p ublished online July 1998 .

Journal Article. Subjects: Mathematics. 0 words.

The operator splitting technique is formulated for inhomogeneous abstract Cauchy problems in Banach spaces, and its convergence properties are analyzed using the concepts, familiar from...

## On a multistep method approximating a linear sectorial evolution equation

in** IMA Journal of Numerical Analysis**

July 2002; p ublished online July 2002 .

Journal Article. Subjects: Mathematics. 0 words.

This paper concerns the linear multistep approximation of an abstract dissipative linear sectorial evolution equation on a Banach space *X*. We study how well the semigroup generated by a...

## ON INTERPOLATION OF THE MEASURE OF NON-COMPACTNESS BY THE COMPLEX METHOD

in** The Quarterly Journal of Mathematics**

March 2015; p ublished online April 2014 .

Journal Article. Subjects: Pure Mathematics. 0 words.

The measure of non-compactness of operators between complex interpolation spaces is studied. An estimate of this measure, under the Calderón approximation condition, is proved. Examples of...

## Estimates for absolutely summing norms of polynomials and multilinear maps

in** The Quarterly Journal of Mathematics**

March 2001; p ublished online March 2001 .

Journal Article. Subjects: Pure Mathematics. 0 words.

We obtain lower bounds for the usual norms and the absolutely summing norms
of polynomials and multilinear mappings from *l*
_{p}
or *c*
_{0} to a Banach space.

Our...

## Noetherian Properties of Fargues-Fontaine Curves

in** International Mathematics Research Notices**

January 2016; p ublished online July 2015 .

Journal Article. Subjects: Mathematics; Pure Mathematics. 10326 words.

We establish that the extended Robba rings associated to a perfect nonarchimedean field of characteristic [math], which arise in [math]-adic Hodge theory as certain completed localizations...

## AMENABILITY AND MODULES FOR ARENS PRODUCT ALGEBRAS

in** The Quarterly Journal of Mathematics**

March 2015; p ublished online June 2014 .

Journal Article. Subjects: Pure Mathematics. 0 words.

Given a Banach algebra *A*, we introduce the notion of a left dual Banach algebra (LDBA) over *A*, and we establish that every LDBA over *A* is a left Arens product algebra over *A*. This can be...