Compactness criteria in quasi-Banach symmetric operator spaces associated with a non-commutative torus
Huang J. Nessipbayev Y. Sukochev F. Zanin D.
1 September 2025Academic Press Inc.
Journal of Functional Analysis
2025#289Issue 5
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.
(Non-commutative) symmetric spaces , Compactness , Equicontinuity , Quasi-Banach spaces
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Institute for Advanced Study in Mathematics, HIT, Harbin, 150001, China
School of Mathematics and Statistics, University of New South Wales, Kensington, 2052, NSW, Australia
Institute of Mathematics and Mathematical Modeling, Almaty, 050010, Kazakhstan
Institute for Advanced Study in Mathematics
School of Mathematics and Statistics
Institute of Mathematics and Mathematical Modeling
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