Composition operators on some semi-Hilbert spaces

2025/08/07 by Estaremi, Y., Ghafri, M. S. Al
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2508.05042

Abstract

This paper investigates composition operators and weighted composition operators on semi-Hilbert spaces induced by positive multiplication operators on \( L²(μ) \). Within the framework of \( A \)-adjoint operators, we characterize conditions under which a composition operator \( C_φ\) is \( A \)-selfadjoint, \( A \)-normal, \( A \)-quasinormal, or \( A \)-unitary, where \( A = M_u \) denotes a positive multiplication operator. Additionally, we provide necessary and sufficient conditions for \( C_φ\) to be an \( A \)-isometry or an \( A \)-partial isometry. Analogous results are also obtained when \( A \) is a positive composition operator. Several examples are presented to illustrate the applicability of the main results.

Citations

• On (N,M)-a-normal And (N, M)-a-quasinormal Semi- Hilbert Space Operators
• Multiplication and composition operators between two Orlicz spaces

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