The ball-covering property of non-commutative spaces of operators on Banach spaces
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| Názov: | The ball-covering property of non-commutative spaces of operators on Banach spaces |
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| Autori: | Bao, Qiyao, Liu, Rui, Shen, Jie |
| Zdroj: | Banach Journal of Mathematical Analysis. 19 |
| Publication Status: | Preprint |
| Informácie o vydavateľovi: | Springer Science and Business Media LLC, 2025. |
| Rok vydania: | 2025 |
| Predmety: | Mathematics - Functional Analysis, Geometry and structure of normed linear spaces, unconditional bases, Summability and bases, functional analytic aspects of frames in Banach and Hilbert spaces, FOS: Mathematics, Calkin algebra, non-commutative spaces of operators, ball-covering property, Spaces of operators, tensor products, approximation properties, 46B20, 46B15, 46B28, Noncommutative function spaces, quotient Banach algebras, Functional Analysis (math.FA) |
| Popis: | A Banach space is said to have the ball-covering property (BCP) if its unit sphere can be covered by countably many closed or open balls off the origin. Let $X$ be a Banach space with a shrinking $1$-unconditional basis. In this paper, by constructing an equivalent norm on $B(X)$, we prove that the quotient Banach algebra $B(X)/K(X)$ fails the BCP. In particular, the result implies that the Calkin algebra $B(H)/ K(H)$, $B(\ell^p)/K(\ell^p)$ ($1 \leq p |
| Druh dokumentu: | Article |
| Popis súboru: | application/xml |
| Jazyk: | English |
| ISSN: | 1735-8787 2662-2033 |
| DOI: | 10.1007/s43037-025-00421-w |
| DOI: | 10.48550/arxiv.2412.07137 |
| Prístupová URL adresa: | http://arxiv.org/abs/2412.07137 |
| Rights: | Springer Nature TDM arXiv Non-Exclusive Distribution |
| Prístupové číslo: | edsair.doi.dedup.....74c15b4a77a9d82b33de5191c9008d56 |
| Databáza: | OpenAIRE |
Nájsť tento článok vo Web of Science | Abstrakt: | A Banach space is said to have the ball-covering property (BCP) if its unit sphere can be covered by countably many closed or open balls off the origin. Let $X$ be a Banach space with a shrinking $1$-unconditional basis. In this paper, by constructing an equivalent norm on $B(X)$, we prove that the quotient Banach algebra $B(X)/K(X)$ fails the BCP. In particular, the result implies that the Calkin algebra $B(H)/ K(H)$, $B(\ell^p)/K(\ell^p)$ ($1 \leq p |
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| ISSN: | 17358787 26622033 |
| DOI: | 10.1007/s43037-025-00421-w |