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

✍ Scribed by Ya.I. Alber

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 484 KB
• Volume: 11
• Category: Article
• ISSN: 0893-9659
• DOI: 10.1016/s0893-9659(98)00112-8

✦ Synopsis

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.