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)

 

 

$ L\sp{1}(I,\,X)$ with order convolution


Authors: R. K. Dhar and H. L. Vasudeva
Journal: Proc. Amer. Math. Soc. 83 (1981), 499-505
MSC: Primary 46J99; Secondary 43A20
DOI: https://doi.org/10.1090/S0002-9939-1981-0627678-X
MathSciNet review: 627678
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that the maximal ideal space of $ {L^1}(I,X)$ is $ (0,1] \times \mathfrak{M}(X)$, where $ \mathfrak{M}(X)$ denotes the maximal ideal space of the Banach algebra $ X$. The Gelfand topology on the Carrier space $ (0,1] \times \mathfrak{M}(X)$ coincides with the topology which is the product of the interval topology in $ (0,1]$ and the Gelfand topology on $ \mathfrak{M}(X)$. Moreover, the Gelfand transform has the form of an indefinite integral.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46J99, 43A20

Retrieve articles in all journals with MSC: 46J99, 43A20


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1981-0627678-X
Article copyright: © Copyright 1981 American Mathematical Society