Banach spaces of homogeneous polynomials without the approximation property

Seán Dineen; Jorge Mujica

Czechoslovak Mathematical Journal (2015)

  • Volume: 65, Issue: 2, page 367-374
  • ISSN: 0011-4642

Abstract

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We present simple proofs that spaces of homogeneous polynomials on L p [ 0 , 1 ] and ℓ 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).

How to cite

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Dineen, Seán, and Mujica, Jorge. "Banach spaces of homogeneous polynomials without the approximation property." Czechoslovak Mathematical Journal 65.2 (2015): 367-374. <http://eudml.org/doc/270087>.

@article{Dineen2015,
abstract = {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).},
author = {Dineen, Seán, Mujica, Jorge},
journal = {Czechoslovak Mathematical Journal},
keywords = {Banach space; approximation property; linear operator; homogeneous polynomial; holomorphic function; Banach spaces; approximation property; linear operators; homogeneous polynomials; holomorphic functions},
language = {eng},
number = {2},
pages = {367-374},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Banach spaces of homogeneous polynomials without the approximation property},
url = {http://eudml.org/doc/270087},
volume = {65},
year = {2015},
}

TY - JOUR
AU - Dineen, Seán
AU - Mujica, Jorge
TI - Banach spaces of homogeneous polynomials without the approximation property
JO - Czechoslovak Mathematical Journal
PY - 2015
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 65
IS - 2
SP - 367
EP - 374
AB - 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).
LA - eng
KW - Banach space; approximation property; linear operator; homogeneous polynomial; holomorphic function; Banach spaces; approximation property; linear operators; homogeneous polynomials; holomorphic functions
UR - http://eudml.org/doc/270087
ER -

References

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