2024/03/04 by Sudip Ranjan Bhuia, Bhuia, Sudip Ranjan
Computer Science · Mathematics · #47B15 #Advanced Topics in Algebra #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #Matrix Theory and Algorithms #Primary 47A65 #Secondary 47A68
paper · pdf · doi:10.48550/arxiv.2403.02207
openalex publication_date 2024/03/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A conjugation C is an anti-linear isometric involution on a complex Hilbert space \clh, and T∈ \clb(\clh) is conjugate normal if T^*T = CTT^*C holds for some conjugation (C). In this paper, we provide a factorization and range inclusion theorem for anti-linear operators, and consequently, establish the polar decomposition for anti-linear operators by applying the Douglas theorem on majorization of Hilbert space operators. Moreover, we present a factorization of C-normal operators based on the polar decomposition. Lastly, we study the Cartesian decomposition of conjugate normal operators, thereby expanding the results in [18].