Completely reducible operators that commute with compact operators
HTML articles powered by AMS MathViewer
- by Shlomo Rosenoer
- Trans. Amer. Math. Soc. 299 (1987), 33-40
- DOI: https://doi.org/10.1090/S0002-9947-1987-0869397-0
- PDF | Request permission
Abstract:
It is shown that if $T$ is a completely reducible operator on a Banach space and $TK = KT$, where $K$ is an injective compact operator with a dense range, then $T$ is a scalar type spectral operator. Other related results are also obtained.References
- Che Kao Fong, Operator algebras with complemented invariant subspace lattices, Indiana Univ. Math. J. 26 (1977), no. 6, 1045–1056. MR 470694, DOI 10.1512/iumj.1977.26.26084
- A. I. Loginov and V. S. Šul′man, Reductive operators and operator algebras, Izv. Akad. Nauk SSSR Ser. Mat. 40 (1976), no. 4, 845–854, 950 (Russian). MR 0428064 V. J. Lomonosov, Invariant subspaces for the family of operators which commute with a completely continuous operator, Funct. Anal. Appl. 7 (1973), 213-214.
- Shlomo Rosenoer, Completely reducible operator algebras and spectral synthesis, Canadian J. Math. 34 (1982), no. 5, 1025–1035. MR 675677, DOI 10.4153/CJM-1982-074-9
- Peter Rosenthal, On commutants of reductive operator algebras, Duke Math. J. 41 (1974), 829–834. MR 358395
- Peter Rosenthal and A. R. Sourour, On operator algebras containing cyclic Boolean algebras, Pacific J. Math. 70 (1977), no. 1, 243–252. MR 500194
- Peter Rosenthal and A. R. Sourour, On operator algebras containing cyclic Boolean algebras, Pacific J. Math. 70 (1977), no. 1, 243–252. MR 500194
Bibliographic Information
- © Copyright 1987 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 299 (1987), 33-40
- MSC: Primary 47B40; Secondary 47A15, 47D30
- DOI: https://doi.org/10.1090/S0002-9947-1987-0869397-0
- MathSciNet review: 869397