Involutions of ℓ2 and s with unique fixed points
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| Publication date | 10-2020 |
| Journal | Transactions of the American Mathematical Society |
| Volume | Issue number | 373 | 10 |
| Pages (from-to) | 7327-7346 |
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| Abstract | Let σ ℓ2 and σR∞ be the linear involutions of ℓ2 and R∞, respectively, given by the formula x → −x. We prove that although ℓ2 and R∞ are homeomorphic, σℓ2 is not topologically conjugate to σR∞. We proceed to examine the implications of this and give characterizations of the involutions that are conjugate to σℓ2 and to σR∞. We show that the linear involution x → −x of a separable, infinite-dimensional Fréchet space E is topologically conjugate to σℓ2 if and only if E contains an infinite-dimensional Banach subspace and otherwise is linearly conjugate to σR∞. |
| Document type | Article |
| Language | English |
| Published at | https://doi.org/10.1090/tran/8162 |
| Other links | https://www.scopus.com/pages/publications/85092393376 |
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Involutions of ℓ2 and s with unique fixed points (submitted)
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