$L^{1}(I, X)$ with order convolution
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- by R. K. Dhar and H. L. Vasudeva PDF
- Proc. Amer. Math. Soc. 83 (1981), 499-505 Request permission
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
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Additional Information
- © Copyright 1981 American Mathematical Society
- 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