Geodesic
Ideals of homogeneous polynomials and weakly compact approximation property in Banach spaces
Czechoslovak Mathematical Journal, Tome 57 (2007) no. 2, pp. 763-776.

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We show that a Banach space $E$ has the weakly compact approximation property if and only if each continuous Banach-valued polynomial on $E$ can be uniformly approximated on compact sets by homogeneous polynomials which are members of the ideal of homogeneous polynomials generated by weakly compact linear operators. An analogous result is established also for the compact approximation property.
Classification : 46B28, 46G20, 46G25, 47B10, 47L20
Keywords: compact approximation property; weakly compact approximation property; ideals of homogeneous polynomials 
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     author = {\c{C}al{\i}\c{s}kan, Erhan},
     title = {Ideals of homogeneous polynomials and weakly compact approximation property in {Banach} spaces},
     journal = {Czechoslovak Mathematical Journal},
     pages = {763--776},
     publisher = {mathdoc},
     volume = {57},
     number = {2},
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     zbl = {1174.46008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2007__57_2_a17/}
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Çalışkan, Erhan. Ideals of homogeneous polynomials and weakly compact approximation property in Banach spaces. Czechoslovak Mathematical Journal, Tome 57 (2007) no. 2, pp. 763-776. http://geodesic.mathdoc.fr/item/CMJ_2007__57_2_a17/