## Criteria for exponential stability of linear differential equations with positive evolution on ordered Banach spaces

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

September 2010; p ublished online July 2010 .

Journal Article. Subjects: Mathematics. 0 words.

In this paper, the problem of exponential stability of the zero state equilibrium of a linear differential equation defined by an operator-valued function with positive evolution on an...

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## Linear Operators in Banach Spaces

in** Spectral Theory and Differential Operators**

May 2018; p ublished online September 2018 .

Chapter. Subjects: Pure Mathematics. 30346 words.

Three main themes run through this chapter: compact linear operators, measures of non-compactness, and Fredholm and semi-Fredholm maps. Connections are established between these themes so...

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** » ** abstract

## COMPUTABILITY ON NON-SEPARABLE BANACH SPACES AND LANDAU'S THEOREM

in** From Sets and Types to Topology and Analysis**

October 2005; p ublished online September 2007 .

Chapter. Subjects: Logic. 10755 words.

In computable analysis, a computable normed space turns out to be necessarily separable. In classical functional analysis, non-separable spaces occur naturally, for example as dual spaces...

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## Smooth functions and partitions of unity on certain Banach spaces

in** The Quarterly Journal of Mathematics**

December 1996 .

Journal Article. Subjects: Pure Mathematics. 0 words.

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## On the holomorphic rigidity of linear operators on complex Banach spaces

in** The Quarterly Journal of Mathematics**

September 1999; p ublished online September 1999 .

Journal Article. Subjects: Pure Mathematics. 0 words.

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## Convex‐Transitive Banach Spaces, Big Points, and the Duality Mapping

in** The Quarterly Journal of Mathematics**

September 2002; p ublished online September 2002 .

Journal Article. Subjects: Pure Mathematics. 0 words.

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## SMOOTH FUNCTIONS AND PARTITIONS OF UNITY ON CERTAIN BANACH SPACES

in** The Quarterly Journal of Mathematics**

December 1996 .

Journal Article. Subjects: Pure Mathematics. 0 words.

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## A KREIN-ŠMULIAN TYPE RESULT IN BANACH SPACES

in** The Quarterly Journal of Mathematics**

June 1997; p ublished online June 1997 .

Journal Article. Subjects: Pure Mathematics. 0 words.

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## Local convergence of Newton's method in Banach space from the viewpoint of the majorant principle

in** IMA Journal of Numerical Analysis**

July 2009; p ublished online July 2008 .

Journal Article. Subjects: Mathematics. 0 words.

A local convergence analysis of Newton's method for solving nonlinear equations, based on Kantorovich's majorant principle, is presented in this paper. This analysis provides a clear...

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## Sphere Equivalence, Banach Expanders, and Extrapolation

in** International Mathematics Research Notices**

January 2015; p ublished online May 2014 .

Journal Article. Subjects: Mathematics. 6309 words.

We study the Banach spectral gap *λ*
_{1}(*G*;*X*,*p*) of finite graphs *G* for pairs (*X*,*p*) of Banach spaces and exponents. We define the notion of sphere equivalence between Banach spaces...

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** » ** abstract

## Banach algebra

in** The Concise Oxford Dictionary of Mathematics**

January 2014; p ublished online September 2014 .

Reference Entry. Subjects: Pure Mathematics. 37 words.

An algebra on a *Banach space that satisfies the inequality ||*xy*||≤||*x*||.||*y*|| for all elements ...

## Generality and structures in functional analysis: the influence of Stefan Banach

in** The Oxford Handbook of Generality in Mathematics and the Sciences**

July 2016; p ublished online July 2017 .

Article. Subjects: Mathematical and Statistical Physics. 15858 words.

This article examines Stefan Banach’s contributions to the field of functional analysis based on the concept of structure and the multiply-flvored expression of generality that arises in...

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## CONVEX-TRANSITIVITY OF BANACH ALGEBRAS VIA IDEALS

in** The Quarterly Journal of Mathematics**

June 2013; p ublished online January 2012 .

Journal Article. Subjects: Pure Mathematics. 0 words.

We investigate a method for producing concrete convex-transitive Banach spaces. The key idea of the method consists of getting rid of dissymmetries of a given space by taking a carefully...

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## BANACH-LIE ALGEBRAS WITH EXTREMAL ELEMENTS

in** The Quarterly Journal of Mathematics**

March 2011; p ublished online October 2009 .

Journal Article. Subjects: Pure Mathematics. 0 words.

In this paper strongly prime Banach-Lie algebras with extremal elements are described. They turn out to be natural extensions of the classical Banach-Lie algebras of compact operators on...

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## 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*)...

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## UNIFORMLY CONVEX-TRANSITIVE FUNCTION SPACES

in** The Quarterly Journal of Mathematics**

March 2011; p ublished online August 2009 .

Journal Article. Subjects: Pure Mathematics. 0 words.

We introduce a property of Banach spaces, called uniform convex-transitivity, which falls between almost transitivity and convex transitivity. We will provide examples of uniformly...

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## Applications of Summing Inclusion Maps to Interpolation of Operators

in** The Quarterly Journal of Mathematics**

March 2003; p ublished online March 2003 .

Journal Article. Subjects: Pure Mathematics. 0 words.

We study interpolation of operators between abstract real method spaces by using thin Banach ideal properties of the inclusion maps between Banach sequence spaces generating these spaces. An...

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## MAXIMUM MODULUS OF RANDOM POLYNOMIALS

in** The Quarterly Journal of Mathematics**

March 2012; p ublished online August 2010 .

Journal Article. Subjects: Pure Mathematics. 0 words.

We give an upper bound of the expectation of the supremum norm of a homogeneous Bernoulli polynomial on the unit ball of a Banach space. This upper bound depends on the geometry of the...

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##
Unconditionality in spaces of *m*-homogeneous polynomials

in** The Quarterly Journal of Mathematics**

March 2005; p ublished online March 2005 .

Journal Article. Subjects: Pure Mathematics. 0 words.

Let *E* be a Banach space with an unconditional basis. We prove that for *m* ≥ 2 the Banach space P(^{
m
}
*E*) of all *m*-homogeneous polynomials on *E* has an...

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## 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...