Intertwining Operators between Two Orthogonal Projections. (25th October 2020)

• Record Type: Journal Article
• Authors: Deng, Chunyuan; Liang, Wenting
• Is Part Of: Numerical functional analysis and optimization. Volume 41:Number 14(2020)
• Page Start: 1794
• Page End: 1803
• Publication Date: 2020-10-25
• Subjects: Intertwining operator -- orthogonal projection -- unitary operator; 47A05; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2020.1813166
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: Let P and Q be a pair of orthogonal projections. In this note we will prove that there exists a unitary U ∈ B ( H ) such that UP = QU and UQ = PU if and only if dim [ R ( P ) ∩ N ( Q ) ] = dim [ N ( P ) ∩ R ( Q ) ] .