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Nonstandard ideals, unicellularity, and algebras associated with a shift operator. (English. Russian original) Zbl 0258.47029

Semin. Math., V. A. Steklov Math. Inst., Leningrad 19, 91-111 (1970); translation from Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklov 19, 156-195 (1970).

MSC:

47A15 Invariant subspaces of linear operators
46A45 Sequence spaces (including Köthe sequence spaces)
47B20 Subnormal operators, hyponormal operators, etc.
46J20 Ideals, maximal ideals, boundaries
46B15 Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces
46J15 Banach algebras of differentiable or analytic functions, \(H^p\)-spaces