The Mathematical Legacy of Victor Lomonosov: Operator Theory

Book

The Mathematical Legacy of Victor Lomonosov

Operator Theory

Edited by: Richard M. Aron , Eva A. Gallardo Gutiérrez , Miguel Martin , Dmitry Ryabogin , Ilya M. Spitkovsky and Artem Zvavitch

Language: English

Published/Copyright: 2020

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This book is in the series

Volume 2 | Advances in Analysis and Geometry

About this book

The fundamental contributions made by the late Victor Lomonosov in several areas of analysis are revisited in this book, in particular, by presenting new results and future directions from world-recognized specialists in the field. The invariant subspace problem, Burnside’s theorem, and the Bishop-Phelps theorem are discussed in detail. This volume is an essential reference to both researchers and graduate students in mathematical analysis.

Collects works on the fundamental contributions in functional analysis and operator theory made by Victor Lomonosov
Edited by a group of internationally renowned mathematicians
Suitable for wide readership in mathematical analysis

Author / Editor information

R. M. Aron, USA; I. Spitkovsky, UAE; E. Gallardo, Spain; M. Martin, Spain; A. Zvavitch, USA; D. Ryabogin, USA.

Topics

Mathematics Analysis

Publicly Available

Frontmatter
I

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Editors’ Introduction
V

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Per Enflo’s personal thoughts about Victor Lomonosov
VII

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Contents
XI

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1. Bishop–Phelps–Bollobás property for positive operators between classical Banach spaces
1
María D. Acosta and Maryam Soleimani-Mourchehkhorti

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2. Isometric embeddings of finite metric trees into (ℝⁿ, d₁) and (ℝⁿ, d_∞)
15
Asuman Güven Aksoy, Mehmet Kılıç and Şahin Koçak

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3. Iterates of the spherical Aluthge transform of 2-variable weighted shifts
25
Chafiq Benhida and Raúl E. Curto

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4. The freewheeling twisting of Hilbert spaces
43
Jesús M. F. Castillo

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5. A survey of ball-covering property of Banach spaces
67
Lixin Cheng, Wen Zhang and Mikio Kato

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6. A note on the quantitative local version of the log-Brunn–Minkowski inequality
85
Andrea Colesanti and Galyna Livshyts

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7. Spectra of “fattened” open book structures
99
James E. Corbin and Peter Kuchment

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8. On some local Bishop–Phelps–Bollobás properties
109
Sheldon Dantas, Sun Kwang Kim, Han Ju Lee and Martin Mazzitelli

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9. Bounded point derivations of fractional orders
123
Stephen Deterding

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10. Invariant subspaces: some minimal proofs
131
Gilles Godefroy

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11. On the Hypercyclicity Criterion for operators of Read’s type
139
Sophie Grivaux

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12. Three-space problem for strictly convex renormings
149
A. J. Guirao, S. Lajara and S. Troyanski

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13. Norm attaining operators of finite rank
157
Vladimir Kadets, Ginés López, Miguel Martín and Dirk Werner

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14. Isometric copies of ℓⁿ_∞ and ℓⁿ₁ in transportation cost spaces on finite metric spaces
189
Seychelle S. Khan, Mutasim Mim and Mikhail I. Ostrovskii

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15. From Lomonosov lemma to radical approach in joint spectral radius theory
205
Edward Kissin, Victor S. Shulman and Yurii V. Turovskii

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16. Pontryagin–Krein theorem: Lomonosov’s proof and related results
231
Edward Kissin, Victor S. Shulman and Yurii V. Turovskii

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17. Poincaré type and spectral gap inequalities with fractional Laplacians on Hamming cube
251
Dong Li and Alexander Volberg

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18. Spectra of generalized Poisson integral operators on L^p(ℝ⁺)
281
Pedro J. Miana and Jesús Oliva-Maza

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19. Order extreme points and solid convex hulls
297
T. Oikhberg and M. A. Tursi

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20. Universal block tridiagonalization in ℬ(ℋ) and beyond
317
Sasmita Patnaik, Srdjan Petrovic and Gary Weiss

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21. Rademacher-type independence in Boolean algebras
327
Mikhail Popov

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Index
349

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Publishing information

Pages and Images/Illustrations in book

eBook published on:

August 10, 2020

eBook ISBN:

9783110656756

Hardcover published on:

August 10, 2020

Hardcover ISBN:

9783110653397

Pages and Images/Illustrations in book

Front matter:

12

Main content:

352

Illustrations:

19

Tables:

50

https://doi.org/10.1515/9783110656756

eBook ISBN: 9783110656756

Hardcover ISBN: 9783110653397

Keywords for this book

Funktionalanalysis; Invarianter Unterraum; Operatortheorie

Audience(s) for this book

Researchers and graduate students in mathematical analysis.

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Manufacturer information:
Walter de Gruyter GmbH
Genthiner Straße 13
10785 Berlin
productsafety@degruyterbrill.com

The Mathematical Legacy of Victor Lomonosov

Overview

About this book

Author / Editor information

Topics

Table of contents

Frontmatter

Editors’ Introduction

Per Enflo’s personal thoughts about Victor Lomonosov

Contents

1. Bishop–Phelps–Bollobás property for positive operators between classical Banach spaces

2. Isometric embeddings of finite metric trees into (ℝn, d1) and (ℝn, d∞)

3. Iterates of the spherical Aluthge transform of 2-variable weighted shifts

4. The freewheeling twisting of Hilbert spaces

5. A survey of ball-covering property of Banach spaces

6. A note on the quantitative local version of the log-Brunn–Minkowski inequality

7. Spectra of “fattened” open book structures

8. On some local Bishop–Phelps–Bollobás properties

9. Bounded point derivations of fractional orders

10. Invariant subspaces: some minimal proofs

11. On the Hypercyclicity Criterion for operators of Read’s type

12. Three-space problem for strictly convex renormings

13. Norm attaining operators of finite rank

14. Isometric copies of ℓn∞ and ℓn1 in transportation cost spaces on finite metric spaces

15. From Lomonosov lemma to radical approach in joint spectral radius theory

16. Pontryagin–Krein theorem: Lomonosov’s proof and related results

17. Poincaré type and spectral gap inequalities with fractional Laplacians on Hamming cube

18. Spectra of generalized Poisson integral operators on Lp(ℝ+)

19. Order extreme points and solid convex hulls

20. Universal block tridiagonalization in ℬ(ℋ) and beyond

21. Rademacher-type independence in Boolean algebras

Index

Bibliographic data

2. Isometric embeddings of finite metric trees into (ℝⁿ, d₁) and (ℝⁿ, d_∞)

14. Isometric copies of ℓⁿ_∞ and ℓⁿ₁ in transportation cost spaces on finite metric spaces

18. Spectra of generalized Poisson integral operators on L^p(ℝ⁺)