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Keywords:
Banach space; approximation property; linear operator; homogeneous polynomial; holomorphic function
Banach space; approximation property; linear operator; homogeneous polynomial; holomorphic function
Summary:
We present simple proofs that spaces of homogeneous polynomials on $L_{p}[0,1]$ and $\ell _{p}$ provide plenty of natural examples of Banach spaces without the approximation property. By giving necessary and sufficient conditions, our results bring to completion, at least for an important collection of Banach spaces, a circle of results begun in 1976 by R. Aron and M. Schottenloher (1976).
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