Generalizations of Kaplansky Theorem for some (p,k)-Quasihyponormal Operators

TL;DR

This paper extends classical operator theory by generalizing bounded operators to unbounded ones and broadens Kaplansky's theorem to include (p,k)-quasihyponormal operators, enhancing understanding of their product properties.

Contribution

It introduces new classes of unbounded operators and generalizes Kaplansky's theorem to (p,k)-quasihyponormal operators, expanding the theoretical framework.

Findings

Extended Kaplansky theorem to (p,k)-quasihyponormal operators.

Defined new notions of unbounded operators like k-quasihyponormal.

Analyzed product properties of these operators.

Abstract

In the present paper, we generalized some notions of bounded operators to un- bounded operators on Hilbert space such as k-quasihyponormal and k-paranormal unbounded operators. Furthermore, we extend the Kaplansky theorem for normal operators to some (p; k)-quasihyponormal operators. Namely the (p; k)-quasihyponormality of the product AB and BA for two operators.