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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.
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참고문헌 (18)
참고문헌 신청
A. F. Ber / 2011 / Derivations in algebras of operator-valued functions / J. Operator Theory 66 (2) : 261 ~ 300
A. G. Kusraev / 1985 / Vector Duality and Its Applications / Nauka
A. G. Kusraev / 2000 / Cyclically compact operators in Banach spaces / Vladikavkaz Math. J 2 (1) : 10 ~ 23
A. G. Kusraev / 2000 / Dominated Operators / Kluwer Academic Publishers
I. G. Ganiev / 2001 / Measurable bundles of compact operators / Methods Funct. Anal. Topology 7 (4) : 1 ~ 5
A. G. Kusraev / 1985 / Vector Duality and Its Applications / Nauka
A. G. Kusraev / 2000 / Cyclically compact operators in Banach spaces / Vladikavkaz Math. J 2 (1) : 10 ~ 23
A. G. Kusraev / 2000 / Dominated Operators / Kluwer Academic Publishers
I. G. Ganiev / 2001 / Measurable bundles of compact operators / Methods Funct. Anal. Topology 7 (4) : 1 ~ 5
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