Projection operators nearly orthogonal to their symmetries

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:446

Article

Walters, Sam¹ 

[1] Univ Northern BC, Dept Math & Stat, Prince George, BC V2N 4Z9, Canada

关键词: Hilbert space;    Norm approximation;    C*-algebras;    Automorphisms;    Projections;    Orthogonality;   

DOI  :  10.1016/j.jmaa.2016.09.013

来源: Elsevier

【 摘 要 】

For any order 2 automorphism a of a C*-algebra A (a symmetry of A), we prove that for each projection e such that parallel to e alpha(e)parallel to <= 9/20, there exists a projection q with q alpha(q) = 0 satisfying the norm estimate parallel to e - q parallel to <= 1/2 parallel to e alpha(e)parallel to + 4 parallel to e alpha(e)parallel to(2). In other words, if a is a projection that is nearly orthogonal to its symmetry a(e) in the sense that the norm parallel to e alpha(e)parallel to is no more than 9/20, then e can be approximated by a projection q that is exactly orthogonal to its symmetry in a fairly optimal fashion. (Optimal in the sense that the first term in the estimate satisfies 1/2 parallel to e alpha(e)parallel to < parallel to e - q parallel to for any such q.) (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free