General explicit expressions for intertwining operators and direct rotations of two orthogonal projections

2017/05/16 by Yan-Ni Dou, Dou, Yan-Ni, Weijuan Shi +7
Computer Science · Decision Sciences · Mathematics · Physics and Astronomy · #47A05 #FOS: Mathematics #Functional Analysis (math.FA) #Matrix Theory and Algorithms #Scientific Measurement and Uncertainty Evaluation #Scientific Research and Discoveries #Spectral Theory (math.SP) #math.FA #math.SP #msc:47A05

paper · pdf · doi:10.48550/arxiv.1705.05870

arxiv created 2017/05/16 · openalex publication_date 2017/05/16 · arxiv updated 2017/05/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, based on the block operator technique and operator spectral theory, the general explicit expressions for intertwining operators and direct rotations of two orthogonal projections have been established. As a consequence, it is an improvement of Kato's result (Perturbation Theory of Linear operators, Springer-Verlag, Berlin/Heidelberg, 1996); J. Avron, R. Seiler and B. Simon's Theorem 2.3 (The index of a pair of projections, J. Funct. Anal. 120(1994) 220-237) and C. Davis, W.M. Kahan, (The rotation of eigenvectors by a perturbation, III. SIAM J. Numer. Anal. 7(1970) 1-46).

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