Norming points and unique minimality of orthogonal projections

Shekhtman, Boris; Skrzypek, Lesław

doi:https://doi.org/10.1155/AAA/2006/42305

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Volume 2006 | Article ID 042305 | https://doi.org/10.1155/AAA/2006/42305

Norming points and unique minimality of orthogonal projections

Boris Shekhtman¹and Lesław Skrzypek¹

Received05 Mar 2005

Accepted06 Apr 2005

Published22 Feb 2006

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.

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Copyright

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.

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