Document Zbl 1030.47052

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Cyclically compact operators in Banach spaces. (English) Zbl 1030.47052

Vladikavkaz. Mat. Zh. 2, No. 1, 10-23 (2000).

Summary: The Boolean-valued interpretation of compactness gives rise to the new notions of cyclically compact sets and operators which deserves an independent study. A part of the corresponding theory is presented in this paper. The general form of compact operators in a Kaplansky-Hilbert module as well as a variant of the Fredholm alternative for cyclically compact operators are given.

Cited in 1 Review

Cited in 5 Documents

MSC:

47S20	Nonstandard operator theory
46S20	Nonstandard functional analysis
03H05	Nonstandard models in mathematics

Keywords:

complete Boolean algebra; normed B-space; mixing; bounded descent

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