ON GENERALIZED SINGULAR NUMBER OF POSITIVE MATRIX OF τ MEASURABLE OPERATORS

Alday M. Raikhan M.
2023 Element D.O.O.

Journal of Mathematical Inequalities
2023 #17 Issue 3 1007 - 1016 pp.

Let (M,τ) be a semi-finite von Neumann algebra, Lo(M) be the set of all τ-measurable operators. We studied generalized singular numbers of 2 × 2 positive matrices with entries in L0 (M). We proved the equivalence of several inequalities associated with these generalized singular numbers and gave symmetric norm’s version of this results, i.e., we extend the related inequalities of 2 × 2 positive semi-definite block matrices in [1, 5] to the 2× 2 positive matrices of τ -measurable operators case.

Generalized singular number , noncommutative symmetric space , positive matrix of τ -measurable operators , semi-finite von Neumann algebra , symmetric space , τ-measurable operator

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Faculty of Mechanics and Mathematics, L. N. Gumilyov Eurasian National University, Astana, 010008, Kazakhstan
Astana IT University, Astana, 010000, Kazakhstan

Faculty of Mechanics and Mathematics
Astana IT University

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