A Class of algebras admitting infinitely many norm topologies

J. G. Patel

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arXiv · 2602.16404

A Class of algebras admitting infinitely many norm topologies

J. G. Patel

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Abstract

Let $\mathcal{A}$ be an algebra, and let $\mathcal{A}^2 =$ span$\{ab : a, b \in \mathcal{A}\}$ be a subalgebra of $\mathcal{A}$. In this paper, we prove that if $\mathcal{A}^2$ has infinite codimension in $\mathcal{A}$ iff $\mathcal{A}$ has discontinuous square annihilation property (DSAP). In fact, in this case, the algebra $\mathcal{A}$ admits infinitely many non-equivalent algebra norms.

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J. G. Patel. 2026-02-18. A Class of algebras admitting infinitely many norm topologies. https://arxiv.org/abs/2602.16404

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