This article is cited in 3 papers

Halmos problems and related results in the theory of invariant subspaces

V. I. Lomonosov^a, V. S. Shulman<sup>b

a</sup> Kent State University, USA
^b Vologda State University

Abstract: This paper contains a survey of main results in the theory of invariant subspaces that have a direct or intermediate connection with the well-known list of problems in operator theory posed by Halmos in 1970. For most results we present brief proofs, schemes of proofs, or basic ideas of proofs.
Bibliography: 124 titles.

Keywords: Banach space, linear operator, operator algebra, invariant subspace.

UDC: 517

MSC: Primary 47A15; Secondary 47L10, 47L30

Received: 22.08.2017
Revised: 16.10.2017

DOI: 10.4213/rm9793

 English version: Russian Mathematical Surveys, 2018, 73:1, 31–90

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