Dual complementors on Banach algebras
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- by B. J. Tomiuk PDF
- Proc. Amer. Math. Soc. 103 (1988), 815-822 Request permission
Abstract:
We study semisimple annihilator Banach algebras $A$ with a right complementor $p$ such that the mapping $q$ on the closed left ideals $J$ of $A$ given by ${J^q} = {l_A}({[{r_A}(J)]^p})$ is a left complementor on $A$. A right complementor $p$ with this property is called dual, and the pair $(p,q)$ is called a dual pair of complementors on $A$.References
- Freda E. Alexander, On complemented and annihilator algebras, Glasgow Math. J. 10 (1969), 38–45. MR 244772, DOI 10.1017/S0017089500000501
- F. E. Alexander and B. J. Tomiuk, Complemented $B^{\ast }$-algebras, Trans. Amer. Math. Soc. 137 (1969), 459–480. MR 236714, DOI 10.1090/S0002-9947-1969-0236714-3
- Bruce A. Barnes, Banach algebras which are ideals in a Banach algebra, Pacific J. Math. 38 (1971), 1–7; correction, ibid. 39 (1971), 828. MR 310640
- F. F. Bonsall and A. W. Goldie, Annihilator algebras, Proc. London Math. Soc. (3) 4 (1954), 154–167. MR 61768, DOI 10.1112/plms/s3-4.1.154
- Jacques Dixmier, Les $C^{\ast }$-algèbres et leurs représentations, Cahiers Scientifiques, Fasc. XXIX, Gauthier-Villars & Cie, Éditeur-Imprimeur, Paris, 1964 (French). MR 0171173
- Irving Kaplansky, The structure of certain operator algebras, Trans. Amer. Math. Soc. 70 (1951), 219–255. MR 42066, DOI 10.1090/S0002-9947-1951-0042066-0
- Michael Leinert, A contribution to Segal algebras, Manuscripta Math. 10 (1973), 297–306. MR 324416, DOI 10.1007/BF01332771
- Charles E. Rickart, General theory of Banach algebras, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London-New York, 1960. MR 0115101
- Bohdan J. Tomiuk, Structure theory of complemented Banach algebras, Canadian J. Math. 14 (1962), 651–659. MR 143060, DOI 10.4153/CJM-1962-055-4
- B. J. Tomiuk, Isomorphisms of multiplier algebras, Glasgow Math. J. 28 (1986), no. 1, 73–77. MR 826630, DOI 10.1017/S0017089500006364
- B. J. Tomiuk, The strong radical and the left regular representation, J. Austral. Math. Soc. Ser. A 43 (1987), no. 1, 1–9. MR 886796
- Bohdan J. Tomiuk and Bertram Yood, Topological algebras with dense socle, J. Functional Analysis 28 (1978), no. 2, 254–277. MR 493387, DOI 10.1016/0022-1236(78)90089-7
Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 103 (1988), 815-822
- MSC: Primary 46H20; Secondary 46K05
- DOI: https://doi.org/10.1090/S0002-9939-1988-0947665-8
- MathSciNet review: 947665