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Open Access Research Article

On class Ak# operators in semi-Hilbertian spaces

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pp. 1–17Online FirstMarch 2026DOI: 10.47974/JIM-2266XML
Received:
01 Feb 2025
Published Online:
26 Mar 2026
Article type:
Research Article
Language:
EN
Article no.:
JIM-2266
Pages:
1–17

Abstract

This paper introduces a novel class of operators in semi-Hilbertian spaces, termed class Ak# operators, which generalizes the well-studied A-hyponormal operators and extends recent developments in operator theory. We define an operator Γ to belong to the class Ak#  if there exists a positive integer k such that  Γ#k Γk ≥A (ΓΓ#)k Central to this work is the exploration of fundamental properties of this class , its relationship to other operator families. We provide concrete examples to demonstrate the non-triviality and applicability of this class, alongside an in-depth analysis of its stability under tensor product operations. Specifically, we establish sufficient conditions under which the tensor product of two class Ak#  operators preserves the class property. These contributions not unify and extend prior results on operator classes but also offer new insights into their structural and functional. 

Keywords

Subject Classifications

Primary 46C50Secondary 47B0247A80

References

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