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DOI: 10.23671/VNC.2016.2.7386

# Trace class and Lidskii trace formula on Kaplansky-Hilbert modules

Gonullu U.
Vladikavkaz Mathematical Journal 2014. Vol. 16. Issue 2.
Abstract:
In this paper, we introduce and study the concepts of the trace class operators and global eigenvalue of continuous $$\Lambda$$-linear operators in Kaplansky-Hilbert modules. In particular, we give a variant of Lidskii trace formula for cyclically compact operators in Kaplansky-Hilbert modules.
Keywords: Kaplansky-Hilbert module, cyclically compact operator, global eigenvalue, trace class, Lidskii trace formula.