Annales Academię Scientiarum Fennicę

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* 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* H^{1} 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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