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MINIMAL SHAPE-PRESERVING PROJECTIONS ONTO ∏n: GENERALIZATIONS AND EXTENSIONS.
- Source :
- Numerical Functional Analysis & Optimization; Nov2006, Vol. 27 Issue 7/8, p847-873, 27p
- Publication Year :
- 2006
-
Abstract
- The goal of this paper is to further the investigation begun in Chalmers and Prophet, Numer. Funct. Anal. Optimiz. 1997; 18:507–520. With the benefit of nearly 10 years of work, we begin by indicating how several proofs from Chalmers and Prophet, Numer. Funct. Anal. Optimiz. 1997; 18:507–520, can be substantially improved. We show that the problem of preserving k-convexity onto Π<subscript>n</subscript> is one part of a larger shape-preserving problem (multiconvex preservation) relative to Π<subscript>n</subscript>, and we completely solve this expanded problem. And finally, we demonstrate that multiconvex preserving projections constructed in this paper are in fact of minimal operator norm in a large class of Banach spaces. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 01630563
- Volume :
- 27
- Issue :
- 7/8
- Database :
- Complementary Index
- Journal :
- Numerical Functional Analysis & Optimization
- Publication Type :
- Academic Journal
- Accession number :
- 23877811
- Full Text :
- https://doi.org/10.1080/01630560600884471