Geodesic
Banach spaces of homogeneous polynomials without the approximation property
Czechoslovak Mathematical Journal, Tome 65 (2015) no. 2, pp. 367-374
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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).
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).
DOI : 10.1007/s10587-015-0181-6
Classification : 46B28, 46G20, 46G25
Keywords: Banach space; approximation property; linear operator; homogeneous polynomial; holomorphic function 
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Dineen, Seán; Mujica, Jorge. Banach spaces of homogeneous polynomials without the approximation property. Czechoslovak Mathematical Journal, Tome 65 (2015) no. 2, pp. 367-374. doi: 10.1007/s10587-015-0181-6

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