Gelfand numbers of embeddings of schatten classes

Aicke Hinrichs; Joscha Prochno; Jan Vybíral

doi:10.1007/s00208-021-02203-9

Gelfand numbers of embeddings of schatten classes

Aicke Hinrichs, Joscha Prochno, Jan Vybíral

Department of Functional Analysis

Research output: Contribution to journal › Article › peer-review

Abstract

Let 0<p,q≤∞ and denote by SNp and SNq the corresponding Schatten classes of real N×N matrices. We study the Gelfand numbers of natural identities SNp↪SNq between Schatten classes and prove asymptotically sharp bounds up to constants only depending on p and q. This extends classical results for finite-dimensional ℓp sequence spaces by E. Gluskin to the non-commutative setting and complements bounds previously obtained by B. Carl and A. Defant, A. Hinrichs and C. Michels, and J. Chávez-Domínguez and D. Kutzarova.

Original language	English
Pages (from-to)	1563–1593
Number of pages	30
Journal	Mathematische Annalen
Volume	380
Issue number	3-4
DOIs	https://doi.org/10.1007/s00208-021-02203-9
Publication status	Published - 2021

Fields of science

101002 Analysis
101032 Functional analysis

JKU Focus areas

Digital Transformation

Access to Document

10.1007/s00208-021-02203-9

Cite this

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title = "Gelfand numbers of embeddings of schatten classes",

abstract = "Let 0<p,q≤∞ and denote by SNp and SNq the corresponding Schatten classes of real N×N matrices. We study the Gelfand numbers of natural identities SNp↪SNq between Schatten classes and prove asymptotically sharp bounds up to constants only depending on p and q. This extends classical results for finite-dimensional ℓp sequence spaces by E. Gluskin to the non-commutative setting and complements bounds previously obtained by B. Carl and A. Defant, A. Hinrichs and C. Michels, and J. Ch{\'a}vez-Dom{\'i}nguez and D. Kutzarova.",

author = "Aicke Hinrichs and Joscha Prochno and Jan Vyb{\'i}ral",

year = "2021",

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language = "English",

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journal = "Mathematische Annalen",

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AU - Hinrichs, Aicke

AU - Prochno, Joscha

AU - Vybíral, Jan

PY - 2021

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N2 - Let 0<p,q≤∞ and denote by SNp and SNq the corresponding Schatten classes of real N×N matrices. We study the Gelfand numbers of natural identities SNp↪SNq between Schatten classes and prove asymptotically sharp bounds up to constants only depending on p and q. This extends classical results for finite-dimensional ℓp sequence spaces by E. Gluskin to the non-commutative setting and complements bounds previously obtained by B. Carl and A. Defant, A. Hinrichs and C. Michels, and J. Chávez-Domínguez and D. Kutzarova.

AB - Let 0<p,q≤∞ and denote by SNp and SNq the corresponding Schatten classes of real N×N matrices. We study the Gelfand numbers of natural identities SNp↪SNq between Schatten classes and prove asymptotically sharp bounds up to constants only depending on p and q. This extends classical results for finite-dimensional ℓp sequence spaces by E. Gluskin to the non-commutative setting and complements bounds previously obtained by B. Carl and A. Defant, A. Hinrichs and C. Michels, and J. Chávez-Domínguez and D. Kutzarova.

U2 - 10.1007/s00208-021-02203-9

DO - 10.1007/s00208-021-02203-9

M3 - Article

SN - 0025-5831

VL - 380

SP - 1563

EP - 1593

JO - Mathematische Annalen

JF - Mathematische Annalen

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ER -