Compactness criteria in quasi-Banach symmetric operator spaces associated with a non-commutative torus

J. Huang; Y. Nessipbayev; F. Sukochev; D. Zanin

doi:10.1016/j.jfa.2025.110946

Compactness criteria in quasi-Banach symmetric operator spaces associated with a non-commutative torus

J. Huang
, Y. Nessipbayev^*
, F. Sukochev
, D. Zanin

^*Corresponding author for this work

Institute for Advanced Study in Mathematics
University of New South Wales
Institute of Mathematics and Mathematical Modelling

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

1 Scopus citations

Abstract

We present two new compactness criteria in non-commutative quasi-Banach symmetric spaces associated to a finite von Neumann algebra, with focus on the non-commutative torus. The first result is novel, even in the commutative setting; while the second resembles the Kolmogorov–Riesz compactness theorem (see Theorems 4.1 and 5.7, respectively). The work contributes to understanding a conjecture of Brudnyi, adapted here for the non-commutative torus.

Original language	English
Article number	110946
Journal	Journal of Functional Analysis
Volume	289
Issue number	5
DOIs	https://doi.org/10.1016/j.jfa.2025.110946
State	Published - 1 Sep 2025
Externally published	Yes

Keywords

(Non-commutative) symmetric spaces
Compactness
Equicontinuity
Quasi-Banach spaces

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10.1016/j.jfa.2025.110946

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AU - Zanin, D.

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N2 - We present two new compactness criteria in non-commutative quasi-Banach symmetric spaces associated to a finite von Neumann algebra, with focus on the non-commutative torus. The first result is novel, even in the commutative setting; while the second resembles the Kolmogorov–Riesz compactness theorem (see Theorems 4.1 and 5.7, respectively). The work contributes to understanding a conjecture of Brudnyi, adapted here for the non-commutative torus.

AB - We present two new compactness criteria in non-commutative quasi-Banach symmetric spaces associated to a finite von Neumann algebra, with focus on the non-commutative torus. The first result is novel, even in the commutative setting; while the second resembles the Kolmogorov–Riesz compactness theorem (see Theorems 4.1 and 5.7, respectively). The work contributes to understanding a conjecture of Brudnyi, adapted here for the non-commutative torus.

KW - (Non-commutative) symmetric spaces

KW - Compactness

KW - Equicontinuity

KW - Quasi-Banach spaces

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ER -

Compactness criteria in quasi-Banach symmetric operator spaces associated with a non-commutative torus

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Keywords

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