Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Quasi-complemented algebras


Authors: T. Husain and Pak-Ken Wong
Journal: Trans. Amer. Math. Soc. 174 (1972), 141-154
MSC: Primary 46H05
DOI: https://doi.org/10.1090/S0002-9947-1972-0410377-6
MathSciNet review: 0410377
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] F. E. Alexander, Representation theorems for complemented algebras, Trans. Amer. Math. Soc. 148 (1970), 385-397. MR 43 #916. MR 0275159 (43:916)
  • [2] -, On complemented and annihilator algebras, Glasgow J. Math. 10 (1969), 38-45. MR 39 #6086. MR 0244772 (39:6086)
  • [3] F. E. Alexander and B. J. Tomiuk, Complemented $ {B^\ast}$-algebras, Trans. Amer. Math. Soc. 137 (1969), 459-480. MR 38 #5009. MR 0236714 (38:5009)
  • [4] G. F. Bachelis, Homomorphisms of annihilator Banach algebras, Pacific J. Math. 25 (1968), 229-247. MR 39 #6076. MR 0244762 (39:6076)
  • [5] B. A. Barnes, Modular annihilator algebras, Canad J. Math. 18 (1966), 566-578. MR 33 #2681. MR 0194471 (33:2681)
  • [6] J. Dixmier, Les $ {C^\ast}$-algèbres et leurs représentations, Cahiers Scientifiques, fasc. 29, Gauthier-Villars, Paris, 1964. MR 30 #1404. MR 0171173 (30:1404)
  • [7] T. Husain and P. K. Wong, On generalized right modular complemented algebras, Studia Math. 45 (1972) 37-42. MR 0328591 (48:6933)
  • [8] S. Kakutani and G. W. Mackey, Ring and lattice characterizations of complex Hilbert space, Bull. Amer. Math. Soc. 52 (1946), 727-733. MR 8, 31. MR 0016534 (8:31e)
  • [9] T. Ogasawara and K. Yoshinaga, Weakly completely continuous Banach $ ^\ast$-algebras, J. Sci. Hiroshima Univ. Ser. A. 18 (1954), 15-36. MR 16, 1126. MR 0070068 (16:1126d)
  • [10] C. E. Rickart, General theory of Banach algebras, University Series in Higher Math., Van Nostrand, Princeton, N. J. 1960. MR 22 #5903. MR 0115101 (22:5903)
  • [11] B. J. Tomiuk, Structure theory of complemented Banach algebras, Canad. J. Math. 14 (1962), 651-659. MR 26 #626. MR 0143060 (26:626)
  • [12] P. K. Wong, Continuous complementors on $ {B^\ast}$-algebras, Pacific J. Math. 33 (1970), 255-260. MR 0285915 (44:3132)
  • [13] -, On the Arens product and annihilator algebras, Proc. Amer. Math. Soc. 30 (1971), 79-83. MR 0281005 (43:6724)
  • [14] B. Yood, Ideals in topological rings, Canad. J. Math. 16 (1964), 28-45. MR 28 #1505. MR 0158279 (28:1505)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 46H05

Retrieve articles in all journals with MSC: 46H05


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1972-0410377-6
Keywords: Quasi-complemented algebras, annihilator and dual algebra, complemented algebra, continuous and uniformly continuous quasi-complementors
Article copyright: © Copyright 1972 American Mathematical Society

American Mathematical Society