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