On $(\alpha,\beta)$-Class (Q) Operators

# Wanjala Victor1 and A. M. Nyongesa1

1Department of Mathematics and Computing, Kibabii University, Bungoma, Kenya.

Abstract: In this paper, we introduce a new class of operator, the class of $(\alpha,\beta)$-Class (Q) operator acting on a complex Hilbert space $H$. An operator $T \in B(H)$ is said to be $(\alpha,\beta)$-Class (Q) if $\alpha^{2}T^{*2}T^{2}\leq (T^{*}T)^{2}\leq \beta^{2}T^{*2}T^{2}$ for $0 \leq \alpha\leq 1 \leq \beta$. We look at some properties that this class are priviledged to enjoy.
Keywords: Class (Q), Normal, $(\alpha,\beta)$-normal, Hypernormal and $(\alpha,\beta)$-Class (Q) operators.

Cite this article as: Wanjala Victor and A. M. Nyongesa, On $(\alpha,\beta)$-Class (Q) Operators, Int. J. Math. And Appl., vol. 9, no. 2, 2021, pp. 111-113.

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