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http://hdl.handle.net/20.500.12128/22422| Title: | Invariant vector means and complementability of Banach spaces in their second duals |
| Authors: | Łukasik, Radosław |
| Keywords: | Commutative semigroup; Invariant mean; Vector-valued mean; Principle of local reflexivity; Banach space complemented in bidual; Commutative cancellative semigroup |
| Issue Date: | 2022 |
| Citation: | "Aequationes Mathematicae", Vol. 96, no. 0, 2022, s. 1-12 |
| Abstract: | Let X be a Banach space. Fix a torsion-free commutative and cancellative semigroup S whose torsion-free rank is the same as the density of X∗∗. We then show that X is complemented in X∗∗ if and only if there exists an invariant mean M:ℓ∞(S,X)→X. This improves upon previous results due to Bustos Domecq (J Math Anal Appl 275(2):512–520, 2002), Kania (J Math Anal Appl 445:797–802, 2017), Goucher and Kania (Studia Math 260:91–101, 2021). |
| URI: | http://hdl.handle.net/20.500.12128/22422 |
| DOI: | 10.1007/s00010-022- 00866-6 |
| ISSN: | 0001-9054 1420-8903 |
| Appears in Collections: | Artykuły (WNŚiT) |
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| File | Description | Size | Format | |
|---|---|---|---|---|
| Lukasik_Invariant_vector_means.pdf | 848,36 kB | Adobe PDF | View/Open |
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