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Abstract. The Gleason--Kahane--Żelazko 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.)
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