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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
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.
math.FA2023
Trace formulas in higher dimensions
Arup Chattopadhyay, Saikat Giri, Chandan Pradhan +1
The paper establishes the Krein and Koplienko trace formulas for multivariable operator functions on symmetrically normed ideals of bounded operators. Results are proved for self-a…