On projective tensor products with complemented subspaces isomorphic to \(\ell^ 1\)

DOI10.1007/BF02844512zbMath0882.46009OpenAlexW1965440337MaRDI QIDQ1373414

Juan A. López Molina, Maria José Rivera

Publication date: 17 December 1997

Published in: Rendiconti del Circolo Matemàtico di Palermo. Serie II (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02844512

zbMATH Keywords

projective tensor productcompact mapsinjective tensor productscomplemented copies of \(\ell^ 1\)unconditional finite-dimensional decompositionsweakly \(p\)-absolutely summable sequences

Mathematics Subject Classification ID

Geometry and structure of normed linear spaces (46B20) Classical Banach spaces in the general theory (46B25) Spaces of operators; tensor products; approximation properties (46B28) Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces (46B15) Tensor products in functional analysis (46M05)

Cites Work

• Operators defined on projective and natural tensor products
• Bounded, Montel and compact operators on vector valued Köthe spaces
• Remarks on contractive projections in \(L_{p}\)-spaces
• On quasi-complemented subspaces of Banach spaces, with an appendix on compactness of operators from \(L^{p}(\mu)\) to \(L^{r}(\nu)\)
• Classical Banach spaces
• Bases, lacunary sequences and complemented subspaces in the spaces $L_{p}$
• Sur la réflexivité des produits tensoriels et les sous-espaces des produits tensoriels projectifs.
• The main triangle projection in matrix spaces and its applications
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