On Generalized Posi-class (Q) Operators
A. M. Nyongesa
Department of Pure and Applied Sciences, Maasai Mara University, Kenya.
Victor Wanjala *
Department of Pure and Applied Sciences, Maasai Mara University, Kenya.
*Author to whom correspondence should be addressed.
Abstract
We introduce and study a two-parameter generalization of Posi-Class (Q) operators on complex Hilbert spaces, which we call n-Posi Class (Q) and (n,m)-Posi-Class (Q) operators. These classes capture algebraic relations between powers of an operator and a positive interruptor. We establish structural properties, invariance under standard operator constructions, spectral inequalities and provide several finite-dimensional and infinite-dimensional examples. Several lemmas, propositions and theorems with proofs are included to illustrate the behaviour of these operators in the classical Hilbert space setting.
Keywords: Class (Q), Almost-Class (Q) operators, Posi-Class (Q), posinormal operators