Generalized projections, decompositions, and the Pythagorean-type theorem in Banach spaces

In this paper, we investigate new properties of the generalized projection operators on convex closed cones in uniformly convex and uniformly smooth Banach spaces; establish decompositions theorems for arbitrary elements both in primary and dual spaces; and prove the Banach space analogue of the Pyt...

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Bibliographic Details
Published inApplied mathematics letters Vol. 11; no. 6; pp. 115 - 121
Main Author Alber, Ya.I.
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.11.1998
Subjects
Banach spaces
Basic variational principle for generalized projections
Dual and polar cones
Duality mappings
Generalized projection operators
Lyapunov functionals
Young-Fenchel transformation
Lyapunov functionals
Generalized projection operators
Basic variational principle for generalized projections
Young-Fenchel transformation
Banach spaces
Dual and polar cones
Duality mappings
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Summary:In this paper, we investigate new properties of the generalized projection operators on convex closed cones in uniformly convex and uniformly smooth Banach spaces; establish decompositions theorems for arbitrary elements both in primary and dual spaces; and prove the Banach space analogue of the Pythagorean-type theorem. Earlier, all these results were known only in Hilbert spaces.
ISSN:0893-9659
1873-5452
DOI:10.1016/S0893-9659(98)00112-8