Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Closed subspaces of finite codimension in some function algebras


Authors: Ramesh V. Garimella and N. V. Rao
Journal: Proc. Amer. Math. Soc. 101 (1987), 657-661
MSC: Primary 46J10; Secondary 46J15
DOI: https://doi.org/10.1090/S0002-9939-1987-0911028-0
MathSciNet review: 911028
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We characterize all closed subspaces of finite codimension in some specific types of function algebras e.g. these include $ C(X)$: algebra of continous functions on a compact Hausdorff space, $ {C^n}[a,b]$: the algebra of $ n$-times continuously differentiable functions on the closed interval $ [a,b]$. Our work is a generalization of the well-known Gleason-Kahane-Želazko theorem [3, 6] for subspaces of codimension one in arbitrary unitary Banach algebras.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46J10, 46J15

Retrieve articles in all journals with MSC: 46J10, 46J15


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1987-0911028-0
Keywords: $ {G_\delta }$-set, polynomial ring, irreducible polynomial, Unique factorization domain, function algebras, ideals of finite codimension
Article copyright: © Copyright 1987 American Mathematical Society