# The Criterion of Completely Reducibility for Continuous Representations of Group Algebras

Source: [The Criterion of Completely Reducibility for Continuous Representations of Group Algebras](<https://www.sota2.com/research/paper/68fa4eda1e209131ce95ed6b>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T10:00:52.849Z

Authors: Chilin V.I., Muminov K.K

Published: 2010-08-19T04:42:12.000Z

## Abstract

It is shown that every nonsingular continuous representation of the group algebra $L^{1}(G)$ in Banach spaces is completely reducible if and only if $G$ is a compact group.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1008.3211>)

[PDF](<https://arxiv.org/pdf/1008.3211.pdf>)