Banach spaces of homogeneous polynomials without the approximation property

Czechoslovak Mathematical Journal

Jorge Mujica¹  Seán Dineen² 

[1] Department of Mathematics, Universidade Estadual de Campinas, Rua Sergio Buarque de Holanda 651, 13083-859 Campinas, So Paulo, Brazil;School of Mathematical Sciences, University College Dublin, Science Centre North, Belfield, Dublin4, Ireland

关键词: Banach space;    approximation property;    linear operator;    homogeneous polynomial;    holomorphic function;   

DOI  :  

学科分类：数学（综合）

来源: Akademie Ved Ceske Republiky

【 摘 要 】

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).

【 授权许可】

Unknown