A new version of the Gleason-Kahane-Żelazko theorem in complete random normed algebras. (English) Zbl 1281.46046

Summary: We first present the notion of multiplicative \(L^0\)-linear functions. Moreover, we establish a new version of the Gleason-Kahane-Żelazko theorem in unital complete random normed algebras.


46H25 Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX)
46H05 General theory of topological algebras
15A78 Other algebras built from modules
Full Text: DOI


[1] Gleason AM: A characterization of maximal ideals. J Anal Math 1967, 19: 171–172.
[2] Kahane JP, \.Zelazko W: A characterization of maximal ideals in commutative Banach algebras. Studia Math 1968, 29: 339–343.
[3] Jarosz K: Generalizations of the Gleason-Kahane-\.Zelazko theorem. Rocky Mount J Math 1991, 21(3):915–921.
[4] Tang YH: The Gleason-Kahane-\.Zelazko theorem in a complete random normed algebra. Acta Anal Funct Appl 2011.
[5] Tang YH, Guo TX: Complete random normed algebras. to appear
[6] Dunford N, Schwartz JT: Linear Operators 1. In Interscience. New York; 1957.
[7] Guo TX: Some basic theories of random normed linear spaces and random inner product spaces. Acta Anal Funct Appl 1999, 1: 160–184.
[8] Guo TX: Recent progress in random metric theory and its applications to conditional risk measures. Sci China Ser A 2011, 54: 633–660.
[9] Guo TX: Relations between some basic results derived from two kinds of topologies for a random locally convex module. J Funct Anal 2010, 258: 3024–3047.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.