6533b86cfe1ef96bd12c89d4
RESEARCH PRODUCT
Topological direct sum decompositions of banach spaces
M. Valdiviasubject
Discrete mathematicsDense setDirect sumGeneral MathematicsExistential quantificationBanach spaceBanach manifoldAlgebra over a fieldTopologyLinear subspaceMathematicsdescription
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 |
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1990-10-01 | Israel Journal of Mathematics |