Article
| Title: | The Banach algebra $L^{1}(G)$ and tame functionals (English) |
| Author: | Komisarchik, Matan |
| Language: | English |
| Journal: | Commentationes Mathematicae Universitatis Carolinae |
| ISSN: | 0010-2628 (print) |
| ISSN: | 1213-7243 (online) |
| Volume: | 65 |
| Issue: | 2 |
| Year: | 2024 |
| Pages: | 131-158 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | We give an affirmative answer to a question due to M. Megrelishvili, and show that for every locally compact group $G$ we have Tame$(L^{1}(G)) = $ Tame$(G)$, which means that a functional is tame over $L^{1}(G)$ if and only if it is tame as a function over $G$. In fact, it is proven that for every norm-saturated, convex vector bornology on RUC$_b(G)$, being small as a function and as a functional is the same. This proves that Asp$(L^{1}(G)) = $ Asp$(G)$ and reaffirms a well-known, similar result which states that WAP$(G) = $ WAP$(L^{1}(G))$. (English) |
| Keyword: | weakly almost periodicity |
| Keyword: | functional on Banach algebra |
| Keyword: | bornology |
| Keyword: | Rosenthal space |
| Keyword: | tame family |
| Keyword: | Asplund space |
| Keyword: | group algebra |
| MSC: | 43A20 |
| MSC: | 43A60 |
| MSC: | 46A17 |
| MSC: | 46H05 |
| DOI: | 10.14712/1213-7243.2025.013 |
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| Date available: | 2025-11-12T11:59:52Z |
| Last updated: | 2025-11-14 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/153165 |
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