On reductive algebras containing compact operators
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- by Peter Rosenthal PDF
- Proc. Amer. Math. Soc. 47 (1975), 338-340 Request permission
Abstract:
It is shown that a reductive operator algebra containing an injective compact operator is selfadjoint.References
- V. I. Lomonosov, Invariant subspaces of the family of operators that commute with a completely continuous operator, Funkcional. Anal. i Priložen. 7 (1973), no. 3, 55–56 (Russian). MR 0420305
- Eric A. Nordgren and Peter Rosenthal, Algebras containing unilateral shifts or finite-rank operators, Duke Math. J. 40 (1973), 419–424. MR 317074
- Heydar Radjavi and Peter Rosenthal, A sufficient condition that an operator algebra be self-adjoint, Canadian J. Math. 23 (1971), 588–597. MR 417802, DOI 10.4153/CJM-1971-066-7
- Heydar Radjavi and Peter Rosenthal, Invariant subspaces, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 77, Springer-Verlag, New York-Heidelberg, 1973. MR 0367682
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 47 (1975), 338-340
- MSC: Primary 46L15; Secondary 47A15
- DOI: https://doi.org/10.1090/S0002-9939-1975-0365168-X
- MathSciNet review: 0365168