Algebras with unconditional orthogonal bases
Authors: Taqdir Husain and Saleem Watson
Journal: Proc. Amer. Math. Soc. 79 (1980), 539-545
MSC: Primary 46H10
MathSciNet review: 572297
Abstract: This is a continuation of our study of topological algebras with orthogonal Schauder bases. In the previous paper, the structure of closed ideals was determined and it was shown that the closed-maximal ideal space is homeomorphic with the discrete space of positive integers. Here it is shown that the space of all maximal ideals equipped with the hull-kernel topology is homeomorphic with the Stone-Čech compactification of natural numbers. Among other results it is also proved that the intersection of dense maximal ideals is isomorphic with the topological dual of the algebra under certain conditions.
-  Mahlon M. Day, Normed linear spaces, Academic Press, Inc., Publishers, New York; Springer-Verlag, Berlin-Göttingen-Heidelberg;, 1962. MR 0145316
-  Leonard Gillman and Meyer Jerison, Rings of continuous functions, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London-New York, 1960. MR 0116199
-  T. Husain and S. Watson, Topological algebras with orthogonal bases, Pacific J. Math. (submitted).
-  Ernest A. Michael, Locally multiplicatively-convex topological algebras, Mem. Amer. Math. Soc., No. 11 (1952), 79. MR 0051444
-  Ivan Singer, Bases in Banach spaces. I, Springer-Verlag, New York-Berlin, 1970. Die Grundlehren der mathematischen Wissenschaften, Band 154. MR 0298399
-  Wiesław Żelazko, Banach algebras, Elsevier Publishing Co., Amsterdam-London-New York; PWN–Polish Scientific Publishers, Warsaw, 1973. Translated from the Polish by Marcin E. Kuczma. MR 0448079
- M. M. Day, Normed linear spaces, Academic Press, New York, 1962. MR 0145316 (26:2847)
- L. Gillman and M. Jerison, Rings of continuous functions, Van Nostrand, Princeton, N. J., 1960. MR 0116199 (22:6994)
- T. Husain and S. Watson, Topological algebras with orthogonal bases, Pacific J. Math. (submitted).
- E. A. Michael, Locally multiplicative convex topological algebras, Mem. Amer. Math. Soc. No. 2, 1952. MR 0051444 (14:482a)
- I. Singer, Bases in Banach spaces. I, Springer-Verlag, New York and Berlin, 1970. MR 0298399 (45:7451)
- W. Zelazko, Banach algebras, Elsevier, New York, 1973. MR 0448079 (56:6389)
Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46H10
Retrieve articles in all journals with MSC: 46H10
Keywords: Topological algebras, orthogonal Schauder bases, maximal ideal space
Article copyright: © Copyright 1980 American Mathematical Society