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Bull. Korean Math. Soc. 2017; 54(2): 679-686
Online first article March 9, 2017 Printed March 31, 2017
https://doi.org/10.4134/BKMS.b160277
Copyright © The Korean Mathematical Society.
Self-adjoint cyclically compact operators and its application
Karimbergen Kudaybergenov and Farrukh Mukhamedov
Karakalpak State University, The United Arab Emirates University
The present paper is devoted to self-adjoint cyclically compact operators on Hilbert--Kaplansky module over a ring of bounded measurable functions. The spectral theorem for such a class of operators is given. We use more simple and constructive method, which allowed to apply this result to compact operators relative to von Neumann algebras. Namely, a general form of compact operators relative to a type I von Neumann algebra is given.
Keywords: compact operator, cyclically compact operator, von Neumann algebra
MSC numbers: 46A19, 46L09, 47B07, 47C15
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