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$ 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
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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?)

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Additional Information

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

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