Journal of Advanced Mathematical Modeling

Journal of Advanced Mathematical Modeling

Invariantly complemented subspaces of dual a left Banach $G$ module

Document Type : Original Paper

Authors
1 Department of Math, Semnan University
2 Department of Math.
Abstract
Let G be a locally compact topological group, and let A be a left Banach G-module. Our purpose, among the other
things, is to study certain weak$^*$-closed subspaces of $A^*$ to consider when their weak$^*$-closed subspaces are the range of a bounded projection on $A^*$ which commutes with translations and convolutions. One of the main results of this paper implies that a locally compact group G is amenable if and only if whenever S is a weak$^*$-closed translation invariant complemented subspace of $L^\infty(G)$, $S$ is the range of a projection on $L^\infty(G)$ commuting with convolutions.
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  • Receive Date 08 March 2025
  • Revise Date 23 November 2025
  • Accept Date 26 May 2026