On the Dunford-Pettis property of the tensor product of $C(K)$ spaces

DOI10.1090/S0002-9939-00-05662-8zbMath0983.46023arXivmath/0004087MaRDI QIDQ2701628

Fernando Bombal, Ignacio Villanueva

Publication date: 19 February 2001

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0004087

zbMATH Keywords

spaces of continuous functionsDunford-Pettis propertysymmetric tensor productbilinear operatorcompletely continuousprojective tensor productscattered compact spaces

Mathematics Subject Classification ID

Linear operators defined by compactness properties (47B07) Spaces of operators; tensor products; approximation properties (46B28) Radon-Nikodým, Kre?n-Milman and related properties (46B22) Tensor products of (C^*)-algebras (46L06)

Related Items (10)

The alternative Dunford--Pettis property on projective tensor products ⋮ On \(C(K)\) Grothendieck spaces ⋮ Dunford-Pettis type properties and the Grothendieck property for function spaces ⋮ Dunford-Pettis properties, Hilbert spaces and projective tensor products ⋮ Some permanence results of the Dunford-Pettis and Grothendieck properties in lcHs ⋮ The bidual of a tensor product of Banach spaces ⋮ Integral operators on the product of \(C(K)\) spaces. ⋮ Dunford-Pettis like properties on tensor products ⋮ A property of Dunford-Pettis type in topological groups ⋮ The Dunford--Pettis and the Kadec--Klee properties on tensor products of JB*-triples

Cites Work

• New Banach space properties of the disc algebra and \(H^{\infty}\)
• Weakly compact operators on the disc algebra
• The Pełczyński property for tight subspaces
• $H^{∞}$ is a Grothendieck space
• Injective factorization of holomorphic mappings
• Regular multilinear operators onC(K)spaces
• Complementation in spaces of symmetric tensor products and polynomials
• Weakly compact multilinear mappings
• Completely continuous multilinear operators on $C(K)$ spaces
• Estimates by polynomials
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