Abstract and Applied Analysis
Volume 2006 (2006), Article ID 42305, 17 pages
doi:10.1155/AAA/2006/42305

Norming points and unique minimality of orthogonal projections

Boris Shekhtman and Lesław Skrzypek

Department of Mathematics, University of South Florida, 4202 E. Fowler Avenue, PHY 114, Tampa 33620-5700, FL, USA

Received 5 March 2005; Accepted 6 April 2005

Copyright © 2006 Boris Shekhtman and Lesław Skrzypek. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study the norming points and norming functionals of symmetric operators on Lp spaces for p=2m or p=2m/(2m−1). We prove some general result relating uniqueness of minimal projection to the set of norming functionals. As a main application, we obtain that the Fourier projection onto span [1,sin⁡x,cos⁡x] is a unique minimal projection in Lp.