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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.16404 |
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| _version_ | 1866914336790806528 |
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| author | Patel, J. G. |
| author_facet | Patel, J. G. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_16404 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Class of algebras admitting infinitely many norm topologies Patel, J. G. Functional Analysis 46H05, 46H25 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. |
| title | A Class of algebras admitting infinitely many norm topologies |
| topic | Functional Analysis 46H05, 46H25 |
| url | https://arxiv.org/abs/2602.16404 |