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Generalizations of certain nest algebra results. (English) Zbl 0781.47016

The author discusses a generalization of the Hilbert space case to a more general setting of certain theorems concerning a nest algebra \({\mathcal L}\) namely
(a) the solvability of \(Tx=y\) within \(\text{Alg} {\mathcal L}\),
(b) the decomposability of finite rank operators, and
(c) approximability in the strong operator topology of \(\text{Alg} {\mathcal L}\) by its finite ranks.
Motivation for this is the recent trend to investigate well-known and important nest algebra theorem to spaces lacking inner product and projections.
Reviewer: U.Kosel (Freiberg)

MSC:

47A15 Invariant subspaces of linear operators
47L10 Algebras of operators on Banach spaces and other topological linear spaces
47C05 Linear operators in algebras
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