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Operator algebras with strictly cyclic vectors

Abstract

We obtain results concerning the invariant subspaces of strictly cyclic operator algebras. In particular, we show that transitivity of a strictly cyclic algebra implies its strict (and hence even its strong) density.

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Literature cited

  1. 1.

    A. Lambert, “Strictly cyclic operator algebras,” Pacific J. Math.,39, No. 3, 1–7 (1971).

  2. 2.

    C. E. Rickart, General Theory of Banach Algebras, Van Nostrand, Princeton, N. J. (1960).

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Additional information

Translated from Matematicheskie Zametki, Vol. 16, No. 2, pp. 253–257, August, 1974.

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Shul'man, V.S. Operator algebras with strictly cyclic vectors. Mathematical Notes of the Academy of Sciences of the USSR 16, 739–741 (1974). https://doi.org/10.1007/BF01105580

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Keywords

  • Invariant Subspace
  • Operator Algebra
  • Cyclic Operator
  • Cyclic Vector
  • Cyclic Algebra