This article is cited in 4 papers

Trace class and Lidskiĭ trace formula on Kaplansky–Hilbert modules

U. Gönüllü

Department of Mathematics and Computer Science, İstanbul Kültür University, Bakırköy, 34156, İstanbul, TURKEY

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 Lidskiĭ trace formula for cyclically compact operators in Kaplansky–Hilbert modules.

Key words: Kaplansky–Hilbert module, cyclically compact operator, global eigenvalue, trace class, Lidskiĭ trace formula.

UDC: 517.98

MSC: 47B60, 46A19, 46B99, 46L08, 47B07

Received: 15.09.2013

Language: English