ACTA issues

Gleason--Kahane--┼╗elazko theorems in function spaces

Javad Mashreghi, Thomas Ransford

Acta Sci. Math. (Szeged) 84:1-2(2018), 227-238

Abstract. The Gleason--Kahane--┼╗elazko theorem states that a linear functional on a Banach algebra that is non-zero on invertible elements is necessarily a scalar multiple of a character. Recently this theorem has been extended to certain Banach function spaces that are not algebras. In this article we present a brief survey of these extensions.

DOI: 10.14232/actasm-017-323-8

AMS Subject Classification (1991): 15A86; 30H10, 46H05, 46H40, 47B49

Keyword(s): linear functional, character, automatic continuity, Banach algebra, function space, Hardy space, Dirichlet space, reproducing kernel

Received November 17, 2017, and in revised form January 25, 2018. (Registered under 73/2017.)