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.
"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