Compact endomorphisms and closed ideals in Banach algebras
HTML articles powered by AMS MathViewer
- by Sandy Grabiner
- Proc. Amer. Math. Soc. 92 (1984), 547-548
- DOI: https://doi.org/10.1090/S0002-9939-1984-0760943-7
- PDF | Request permission
Abstract:
Every infinite-dimensional Banach algebra with a nonzero compact endomorphism has a proper closed nonzero two-sided ideal. When the algebra is commutative, the ideal is also an ideal in the multiplier algebra.References
- J. Esterle, Quasimultipliers, representations of $H^{\infty }$, and the closed ideal problem for commutative Banach algebras, Radical Banach algebras and automatic continuity (Long Beach, Calif., 1981) Lecture Notes in Math., vol. 975, Springer, Berlin, 1983, pp. 66–162. MR 697579, DOI 10.1007/BFb0064548
- C. K. Fong, E. A. Nordgren, M. Radjabalipour, H. Radjavi, and P. Rosenthal, Extensions of Lomonosov’s invariant subspace theorem, Acta Sci. Math. (Szeged) 41 (1979), no. 1-2, 55–62. MR 534499
- Sandy Grabiner, Derivations and automorphisms of Banach algebras of power series, Memoirs of the American Mathematical Society, No. 146, American Mathematical Society, Providence, R.I., 1974. MR 0415321
- Sandy Grabiner, Operator ranges and invariant subspaces, Indiana Univ. Math. J. 28 (1979), no. 5, 845–857. MR 542341, DOI 10.1512/iumj.1979.28.28059
- Herbert Kamowitz, Compact endomorphisms of Banach algebras, Pacific J. Math. 89 (1980), no. 2, 313–325. MR 599123
- 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
- Carl Pearcy and Allen L. Shields, A survey of the Lomonosov technique in the theory of invariant subspaces, Topics in operator theory, Math. Surveys, No. 13, Amer. Math. Soc., Providence, R.I., 1974, pp. 219–229. MR 0355639
Bibliographic Information
- © Copyright 1984 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 92 (1984), 547-548
- MSC: Primary 46H05; Secondary 46J05, 47A15
- DOI: https://doi.org/10.1090/S0002-9939-1984-0760943-7
- MathSciNet review: 760943