Banach Journal of Mathematical Analysis

Point multipliers and the Gleason–Kahane–Żelazko theorem

Razieh Sadat Ghodrat and Fereshteh Sady

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Let A be a Banach algebra, and let X be a left Banach A-module. In this paper, using the notation of point multipliers on left Banach modules, we introduce a certain type of spectrum for the elements of X and we also introduce a certain subset of X which behaves as the set of invertible elements of a commutative unital Banach algebra. Among other things, we use these sets to give some Gleason–Kahane–Żelazko theorems for left Banach A-modules.

Article information

Banach J. Math. Anal. Volume 11, Number 4 (2017), 864-879.

Received: 3 August 2016
Accepted: 5 December 2016
First available in Project Euclid: 17 August 2017

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Digital Object Identifier

Primary: 46H25: Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX)
Secondary: 47B33: Composition operators 47B48: Operators on Banach algebras

Gleason–Kahane–Żelazko theorem spectrum-preserving maps point multipliers Banach modules function modules


Ghodrat, Razieh Sadat; Sady, Fereshteh. Point multipliers and the Gleason–Kahane–Żelazko theorem. Banach J. Math. Anal. 11 (2017), no. 4, 864--879. doi:10.1215/17358787-2017-0021.

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