most citedSymmetric functionals on simply generated symmetric spaces

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math.FA2024

Extended zeta-function residues on principal ideals

Yongqiang Tian, Alexandr Usachev

We study extended zeta-function residues on principal ideals of compact operators and their connections with Dixmier traces. We establish a Lidskii-type formula for continuous sing…

math.FA2024

Decomposition of the set of Banach limits into discrete and continuous subsets

Nikolai Avdeev, Evgenii Semenov, Alexandr Usachev +1

The aim of this work is to describe subsets of Banach limits in terms of a certain functional characteristic. We compute radii and cardinalities for some of these subsets.

math.FA2024

Dixmier-type traces on semifinite symmetric spaces

Galina Levitina, Alexandr Usachev

We prove that a normalised linear functional on certain semifinite symmetric spaces respects tail majorisation if and only if it is a Dixmier-type trace.