Banach Journal of Mathematical Analysis
- Banach J. Math. Anal.
- Volume 10, Number 3 (2016), 608-620.
Vector-valued characters on vector-valued function algebras
Let be a commutative unital Banach algebra and let be a compact space. We study the class of -valued function algebras on as subalgebras of with certain properties. We introduce the notion of -characters of an -valued function algebra as homomorphisms from into that basically have the same properties as evaluation homomorphisms , with . We show that, under certain conditions, there is a one-to-one correspondence between the set of -characters of and the set of characters of the function algebra of all scalar-valued functions in . For the so-called natural -valued function algebras, such as and , we show that () are the only -characters. Vector-valued characters are utilized to identify vector-valued spectra.
Banach J. Math. Anal., Volume 10, Number 3 (2016), 608-620.
Received: 23 May 2015
Accepted: 27 November 2015
First available in Project Euclid: 22 July 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 46J10: Banach algebras of continuous functions, function algebras [See also 46E25]
Secondary: 46J20: Ideals, maximal ideals, boundaries 46H10: Ideals and subalgebras 46E40: Spaces of vector- and operator-valued functions
Abtahi, Mortaza. Vector-valued characters on vector-valued function algebras. Banach J. Math. Anal. 10 (2016), no. 3, 608--620. doi:10.1215/17358787-3607486. https://projecteuclid.org/euclid.bjma/1469199412