Quasi-complemented algebras

Husain, T.; Wong, Pak-Ken

doi:10.1090/S0002-9947-1972-0410377-6

Quasi-complemented algebras
HTML articles powered by AMS MathViewer

by T. Husain and Pak-Ken Wong PDF

Trans. Amer. Math. Soc. 174 (1972), 141-154 Request permission

Abstract:

In this paper we introduce a class of algebras which we call quasi-complemented algebras. A structure and representation theory is developed. We also study the uniformly continuous quasi-complementors on ${B^\ast }$-algebras.

References

Freda E. Alexander, Representation theorems for complemented algebras, Trans. Amer. Math. Soc. 148 (1970), 385–398. MR 275159, DOI 10.1090/S0002-9947-1970-0275159-5
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
Gregory F. Bachelis, Homomorphisms of annihilator Banach algebras, Pacific J. Math. 25 (1968), 229–247. MR 244762
Bruce A. Barnes, Modular annihilator algebras, Canadian J. Math. 18 (1966), 566–578. MR 194471, DOI 10.4153/CJM-1966-055-6
Jacques Dixmier, Les $C^{\ast }$-algèbres et leurs représentations, Cahiers Scientifiques, Fasc. XXIX, Gauthier-Villars & Cie, Éditeur-Imprimeur, Paris, 1964 (French). MR 0171173
T. Husain and Pak Ken Wong, On generalized right modular complemented algebras, Studia Math. 45 (1973), 37–42. (errata insert). MR 328591, DOI 10.4064/sm-45-1-37-42
Shizuo Kakutani and George W. Mackey, Ring and lattice characterization of complex Hilbert space, Bull. Amer. Math. Soc. 52 (1946), 727–733. MR 16534, DOI 10.1090/S0002-9904-1946-08644-9
Tôzirô Ogasawara and Kyôichi Yoshinaga, Weakly completely continuous Banach $^*$-algebras, J. Sci. Hiroshima Univ. Ser. A 18 (1954), 15–36. MR 70068
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
Pak-ken Wong, Continuous complementors on $B^{\ast }$-algebras, Pacific J. Math. 33 (1970), 255–260. MR 285915
Pak-ken Wong, On the Arens product and annihilator algebras, Proc. Amer. Math. Soc. 30 (1971), 79–83. MR 281005, DOI 10.1090/S0002-9939-1971-0281005-2
Bertram Yood, Ideals in topological rings, Canadian J. Math. 16 (1964), 28–45. MR 158279, DOI 10.4153/CJM-1964-004-2