Uncomplemented subspaces in operator and polynomial ideals

Generalizing a number of known linear and nonlinear results, we establish conditions for the space of linear operators belonging to a given operator ideal not to be complemented in the space of bounded linear operators, and for the space of n -homogeneous polynomials belonging to a given polynomial...

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Bibliographic Details
Published inRevista matemática complutense Vol. 35; no. 3; pp. 851 - 869
Main Authors Botelho, Geraldo, Fávaro, Vinícius V., Pérez, Sergio A.
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 2022
Springer Nature B.V
Subjects
Algebra
Analysis
Applications of Mathematics
Geometry
Linear operators
Mathematics
Mathematics and Statistics
Polynomials
Subspaces
Topology
46B28
47L20
Polynomial ideals
46B20
47B10
Uncomplemented subspaces
Banach spaces
Operator ideals
46G25
47L22
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Summary:Generalizing a number of known linear and nonlinear results, we establish conditions for the space of linear operators belonging to a given operator ideal not to be complemented in the space of bounded linear operators, and for the space of n -homogeneous polynomials belonging to a given polynomial ideal not to be complemented in the space of continuous n -homogeneous polynomials. Illustrative examples are provided.
ISSN:1139-1138
1988-2807
DOI:10.1007/s13163-021-00408-9