Self-adjoint cyclically compact operators and its application
Bull. Korean Math. Soc. 2017 Vol. 54, No. 2, 679-686
Published online March 9, 2017
Printed March 31, 2017
Karimbergen Kudaybergenov and Farrukh Mukhamedov
Karakalpak State University, The United Arab Emirates University
Abstract : 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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