A note on generalized characters

Bhatt, S. J. ; Dedania, H. V. (2001) A note on generalized characters Proceedings of the Indian Academy of Sciences - Mathematical Sciences, 115 (4). pp. 437-444. ISSN 0253-4142

PDF - Publisher Version

Official URL: http://www.ias.ac.in/mathsci/vol115/nov2005/PM2519...

Related URL: http://dx.doi.org/10.1007/BF02829805


For a compactly generated LCA group G, it is shown that the set H(G) of all generalized characters on G equipped with the compact-open topology is a LCA group and H(G) = G^ (the dual group of G) if and only if G is compact. Both results fail for arbitrary LCA groups. Further, if G is second countable, then the Gel'fand space of the commutative convolution algebra Cc (G) equipped with the inductive limit topology is topologically homeomorphic to H(G).

Item Type:Article
Source:Copyright of this article belongs to Indian Academy of Sciences.
Keywords:Compactly Generated LCA Group; Character; Generalized Character; Gel'fand Space; Commutative Topological Algebra
ID Code:59680
Deposited On:07 Sep 2011 05:17
Last Modified:18 May 2016 10:09

Repository Staff Only: item control page