Euclidean Structures and Operator Theory in Banach Spaces / Nigel J. Kalton, Emiel Lorist, and Lutz Weis.

Format:

Book

Author/Creator:

Kalton, Nigel J., 1946- author.

Lorist, Emiel, author.

Weis, Lutz, author.

Series:

Memoirs of the American Mathematical Society ; Volume 288.

Memoirs of the American Mathematical Society Series ; Volume 288

Language:

English

Subjects (All):

Functional analysis.

Geometry.

Physical Description:

1 online resource (168 pages)

Edition:

First edition.

Place of Publication:

Providence, RI : American Mathematical Society, [2023]

Summary:

View the abstract.

Contents:

Cover

Title page

Introduction

The history of Euclidean structures

Structure of the memoir

Notation and conventions

Acknowledgments

Chapter 1. Euclidean structures and -bounded operator families

1.1. Euclidean structures

1.2. -bounded operator families

1.3. The representation of -bounded operator families on a Hilbert space

1.4. The equivalence of -boundedness and *-boundedness

Chapter 2. Factorization of -bounded operator families

2.1. Factorization of - and ₂-bounded operator families

2.2. -bounded operator families on Banach function spaces

2.3. Factorization of ℓ²-bounded operator families through ²( , )

2.4. Banach function space-valued extensions of operators

Chapter 3. Vector-valued function spaces and interpolation

3.1. The spaces ( , ) and (

)

3.2. Function space properties of (

3.3. The -interpolation method

3.4. A comparison with real and complex interpolation

Chapter 4. Sectorial operators and ^{∞}-calculus

4.1. The Dunford calculus

4.2. (Almost) -sectorial operators

4.3. -bounded ^{∞}-calculus

4.4. Operator-valued and joint ^{∞}-calculus

4.5. -bounded imaginary powers

Chapter 5. Sectorial operators and generalized square functions

5.1. Generalized square function estimates

5.2. Dilations of sectorial operators

5.3. A scale of generalized square function spaces

5.4. Generalized square function spaces without almost -sectoriality

Chapter 6. Some counterexamples

6.1. Schauder multiplier operators

6.2. Sectorial operators which are not almost -sectorial

6.3. Almost -sectorial operators which are not -sectorial

6.4. Sectorial operators with _{ ^{∞}}( )&gt

( )

Bibliography

Back Cover.

Notes:

Includes bibliographical references.

Description based on print version record.

Other Format:

Print version: Kalton, Nigel J. Euclidean Structures and Operator Theory in Banach Spaces

ISBN:

1-4704-7575-8