Trace Class and Lidskiĭ trace formula in Kaplansky–Hilbert modules

Abstract

In this paper, we introduce and study the concepts of the trace class op-erators and global eigenvalue of continuous Λ-linear operators in Kaplansky−Hilbertmodules. In particular, we give a variant of Lidski˘ı trace formula for cyclically com-pact operators in a Kaplansky−Hilbert modules.