Annales Academić Scientiarum Fennicć
Mathematica
Volumen 33, 2008, 429-438

NEW EXAMPLES OF WEAKLY COMPACT APPROXIMATION IN BANACH SPACES

Eero Saksman and Hans-Olav Tylli

University of Helsinki, Department of Mathematics and Statistics
P.O. Box 68, FI-00014 University of Helsinki, Finland; eero.saksman 'at' helsinki.fi

University of Helsinki, Department of Mathematics and Statistics
P.O. Box 68, FI-00014 University of Helsinki, Finland; hojtylli 'at' cc.helsinki.fi

Abstract. The Banach space E has the weakly compact approximation property (W.A.P.) if there is C < \infty so that the identity map I_E can be uniformly approximated on any weakly compact subset D \subset E by weakly compact operators V on E satisfying ||V|| \le C. We show that the spaces N(\ell^p,\ell^q) of nuclear operators \ell^p \to \ell^q have the W.A.P. for 1 < q \le p < \infty, but that the Hardy space H¹ does not have the W.A.P.

2000 Mathematics Subject Classification: Primary 46B28; Secondary 46B20.

Key words: Weakly compact approximation, nuclear operators, Hardy space.

Reference to this article: E. Saksman and H.-O. Tylli: New examples of weakly compact approximation in Banach spaces. Ann. Acad. Sci. Fenn. Math. 33 (2008), 429-438.

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