TY - JOUR

T1 - Self-adjoint cyclically compact operators and its application

AU - Kudaybergenov, Karimbergen

AU - Mukhamedov, Farrukh

N1 - Publisher Copyright:
© 2017 Korean Mathematical Society.

PY - 2017

Y1 - 2017

N2 - 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.

AB - 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.

KW - Compact operator

KW - Cyclically compact operator

KW - Von Neumann algebra

UR - http://www.scopus.com/inward/record.url?scp=85016408280&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85016408280&partnerID=8YFLogxK

U2 - 10.4134/BKMS.b160277

DO - 10.4134/BKMS.b160277

M3 - Article

AN - SCOPUS:85016408280

SN - 1015-8634

VL - 54

SP - 679

EP - 686

JO - Bulletin of the Korean Mathematical Society

JF - Bulletin of the Korean Mathematical Society

IS - 2

ER -