The Mathematical Legacy of Victor Lomonosov

Operator Theory

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

• Publisher: De Gruyter
• Year: 2020
• Print ISBN:
  9783110653397
• eBook ISBN:
  9783110653465
• Topic: Mathematics
• Subtopic: Functional Analysis
• Index: Mathematics

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.

Table of contents

• Title Page
• Copyright
• 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 ℓ∞n and ℓ1n 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
• Subject Index