The minus order for idempotents

2019/12/20 by Li, Yuan, Niu, Jiajia, Xu, Xiaoming
#46C20 #47A05 #47B65 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1912.09718

Abstract

Let P and Q be idempotents on a Hilbert space H. The minus order P\preceq Q is defined by the equation PQ=QP=P. In this note, we first present some necessary and sufficient conditions for which the supremum and infimum of idempotents P and Q exist with respect to the minus order. Also, some properties of the minimum Q^or are characterized, where Q^or=min \P^': P^' is an orthogonal projection on H with Q \preceq P^' \.

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