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July 2016 Vector-valued characters on vector-valued function algebras
Mortaza Abtahi
Banach J. Math. Anal. 10(3): 608-620 (July 2016). DOI: 10.1215/17358787-3607486

Abstract

Let A be a commutative unital Banach algebra and let X be a compact space. We study the class of A-valued function algebras on X as subalgebras of C(X,A) with certain properties. We introduce the notion of A-characters of an A-valued function algebra A as homomorphisms from A into A that basically have the same properties as evaluation homomorphisms Ex:ff(x), with xX. We show that, under certain conditions, there is a one-to-one correspondence between the set of A-characters of A and the set of characters of the function algebra A=AC(X) of all scalar-valued functions in A. For the so-called natural A-valued function algebras, such as C(X,A) and Lip(X,A), we show that Ex (xX) are the only A-characters. Vector-valued characters are utilized to identify vector-valued spectra.

Citation

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Mortaza Abtahi. "Vector-valued characters on vector-valued function algebras." Banach J. Math. Anal. 10 (3) 608 - 620, July 2016. https://doi.org/10.1215/17358787-3607486

Information

Received: 23 May 2015; Accepted: 27 November 2015; Published: July 2016
First available in Project Euclid: 22 July 2016

zbMATH: 1365.46048
MathSciNet: MR3528350
Digital Object Identifier: 10.1215/17358787-3607486

Subjects:
Primary: 46J10
Secondary: 46E40, 46H10, 46J20

Rights: Copyright © 2016 Tusi Mathematical Research Group

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Vol.10 • No. 3 • July 2016
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