Complemented subspaces of homogeneous polynomials

Let P K ( n E ; F ) (resp. P w ( n E ; F ) ) denote the subspace of all P ∈ P ( n E ; F ) which are compact (resp. weakly continuous on bounded sets). We show that if P K ( n E ; F ) contains an isomorphic copy of c 0 , then P K ( n E ; F ) is not complemented in P ( n E ; F ) . Likewise we show tha...

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Bibliographic Details
Published inRevista matemática complutense Vol. 31; no. 1; pp. 153 - 161
Main Author Pérez, Sergio A.
Format Journal Article
LanguageEnglish
Published Milan Springer Milan 2018
Springer Nature B.V
Subjects
Algebra
Analysis
Applications of Mathematics
Geometry
Mathematics
Mathematics and Statistics
Subspaces
Topology
Compact operator
46B28
Homogeneous polynomial
Banach space
Linear operator
Unconditional basis
46G25
Complemented subspace
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Summary:Let P K ( n E ; F ) (resp. P w ( n E ; F ) ) denote the subspace of all P ∈ P ( n E ; F ) which are compact (resp. weakly continuous on bounded sets). We show that if P K ( n E ; F ) contains an isomorphic copy of c 0 , then P K ( n E ; F ) is not complemented in P ( n E ; F ) . Likewise we show that if P w ( n E ; F ) contains an isomorphic copy of c 0 , then P w ( n E ; F ) is not complemented in P ( n E ; F ) .
ISSN:1139-1138
1988-2807
DOI:10.1007/s13163-017-0240-7