Self-adjoint cyclically compact operators and their applications

2015/02/09 by Farrukh Mukhamedov, Mukhamedov, Farrukh, Karimbergen Kudaybergenov +1
Mathematics · #45P05 #47B07 #47C15 #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Operator Algebras (math.OA) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1502.02366

openalex publication_date 2015/02/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This 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 are given. We apply this result to partial integral equations on the space with mixed norm of measurable functions and to compact operators relative to von Neumann algebras. We will give a condition of solvability of partial integral equations with self-adjoint kernel. Moreover, a general form of compact operators relative to a type I von Neumann algebra is given.

Citations

• Additive derivations on algebras of measurable operators

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