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J. C. Díaz Alcaide (1990)
Revista Matemática de la Universidad Complutense de Madrid
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Two properties on projective tensor products are introduced and briefly studied. We apply them to give sufficient conditions to assure the non-containment of l1 in a projective tensor product of Banach spaces.
Thomas Kappeler (1986)
Mathematische Zeitschrift
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Wilkins, Dave (1995)
International Journal of Mathematics and Mathematical Sciences
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Surjit Singh Khurana (1981)
Mathematische Zeitschrift
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Diómedes Bárcenas (1991)
Extracta Mathematicae
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G. Groenewegen, A. van Rooij (1987)
Mathematische Zeitschrift
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Giovanni Emmanuele (2004)
Commentationes Mathematicae Universitatis Carolinae
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Using some known lifting theorems we present three-space property type and permanence results; some of them seem to be new, whereas other are improvements of known facts.
V. Caselles (1985)
Mathematische Zeitschrift
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M. Valdivia (1989)
Studia Mathematica
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K. K. Kampoukos, S. K. Mercourakis (2010)
Fundamenta Mathematicae
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A class of Banach spaces, countably determined in their weak topology (hence, WCD spaces) is defined and studied; we call them strongly weakly countably determined (SWCD) Banach spaces. The main results are the following: (i) A separable Banach space not containing ℓ¹(ℕ) is SWCD if and only if it has separable dual; thus in particular, not every separable Banach space is SWCD. (ii) If K is a compact space, then the space C(K) is SWCD if and only if K is countable.