Advances in Operator Theory

A note on irreducible representations of some vector-valued function algebras

Terje Hõim and D‎. ‎A‎. ‎Robbins

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Abstract

‎Let $\pi‎ :‎\mathcal{E}$ $\rightarrow X$ be a bundle of Banach algebras‎, ‎where $X$ is a completely regular Hausdorff space‎. ‎We identify the sets of irreducible representations of several topological subalgebras of $\Gamma(\pi ),$ the space of continuous sections of $\pi‎ .‎$ The results unify recent and older work of various authors regarding representations on algebra-valued function spaces‎.

Article information

Source
Adv. Oper. Theory, Volume 4, Number 2 (2019), 419-427.

Dates
Received: 18 May 2018
Accepted: 25 September 2018
First available in Project Euclid: 1 December 2018

Permanent link to this document
https://projecteuclid.org/euclid.aot/1543633235

Digital Object Identifier
doi:10.15352/aot.1805-1370

Mathematical Reviews number (MathSciNet)
MR3883144

Subjects
Primary: 46H25: Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX)
Secondary: 46H10: Ideals and subalgebras

Keywords
irreducible representation bundle of Banach algebras ‎cover-strict topology‎‎ ‎cover topology

Citation

Hõim, Terje; ‎Robbins, D‎. ‎A‎. A note on irreducible representations of some vector-valued function algebras. Adv. Oper. Theory 4 (2019), no. 2, 419--427. doi:10.15352/aot.1805-1370. https://projecteuclid.org/euclid.aot/1543633235


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