Topological direct sum decompositions of banach spaces

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RESEARCH PRODUCT

Topological direct sum decompositions of banach spaces

subject

Discrete mathematics Dense set Direct sum General Mathematics Existential quantification Banach space Banach manifold Algebra over a field Topology Linear subspace Mathematics

description

LetY andZ be two closed subspaces of a Banach spaceX such thatY≠lcub;0rcub; andY+Z=X. Then, ifZ is weakly countably determined, there exists a continuous projectionT inX such that ∥T∥=1,T(X)⊃Y, T −1(0)⊂Z and densT(X)=densY. It follows that every Banach spaceX is the topological direct sum of two subspacesX 1 andX 2 such thatX 1 is reflexive and densX 2**=densX**/X.

year	journal	country	edition	language
1990-10-01	Israel Journal of Mathematics

https://doi.org/10.1007/bf02773747

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