Approximation numbers of weighted composition operators

被引：7

作者：

Lechner, G. ^{[1
]}

Li, D. ^{[2
]}

Queffelec, H. ^{[3
]}

Rodriguez-Piazza, L. ^{[4
]}

机构：

[1] Cardiff Univ, Sch Math, Cardiff, S Glam, Wales

[2] Univ Artois, LML, Arras, France

[3] Univ Lille Nord France, Lille, France

[4] Univ Seville, Seville, Spain

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2018年 / 274卷 / 07期

关键词：

Composition operators; Approximation numbers; von Neumann algebras; QUANTUM-FIELD THEORIES; HARDY-SPACES; MODULAR STRUCTURES; NUCLEAR MAPS;

D O I：

10.1016/j.jfa.2018.01.010

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the approximation numbers of weighted composition operators f -> w. (f o phi) on the Hardy space H-2 on the unit disc. For general classes of such operators, upper and lower bounds on their approximation numbers are derived. For the special class of weighted lens map composition operators with specific weights, we show how much the weight w can improve the decay rate of the approximation numbers, and give sharp upper and lower bounds. These examples are motivated from applications to the analysis of relative commutants of special inclusions of von Neumann algebras appearing in quantum field theory (Borchers triples). (C) 2018 Elsevier Inc. All rights reserved.

引用

页码：1928 / 1958

页数：31

共 38 条

[1] Inverse Scattering and Local Observable Algebras in Integrable Quantum Field Theories [J].