標題: Sums of orthogonal projections
作者: Choi, Man-Duen
Wu, Pei Yuan
應用數學系
Department of Applied Mathematics
關鍵字: Orthogonal projection;Essential norm;Trace;Rank
公開日期: 15-七月-2014
摘要: In this paper, we consider the problem of characterizing Hilbert space operators which are expressible as a sum of (finitely many) orthogonal projections. We obtain a special operator matrix representation and some necessary/sufficient conditions for an infinite-dimensional operator to be expressible as a sum of projections. We prove that a positive operator with essential norm strictly greater than one is always a sum of projections, and if an injective operator of the form I + K, where K is compact, is a sum of projections, then either trace K+ = trace K- = infinity on or K is of trace class with trace K a nonnegative integer. We also consider sums of those projections which have a fixed rank. The closure of the set of sums of projections is also characterized. (C) 2014 Elsevier Inc. All rights reserved.
URI: http://dx.doi.org/10.1016/j.jfa.2014.05.003
http://hdl.handle.net/11536/24610
ISSN: 0022-1236
DOI: 10.1016/j.jfa.2014.05.003
期刊: JOURNAL OF FUNCTIONAL ANALYSIS
Volume: 267
Issue: 2
起始頁: 384
結束頁: 404
顯示於類別:期刊論文


文件中的檔案:

  1. 000337206900003.pdf