On ($\alpha$,$\beta$)-Class (Q) Operators
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Keywords:
Class (Q), Normal, $(\alpha,\beta)$-normal, Hypernormal and $(\alpha,\beta)$-Class (Q) operatorsAbstract
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.
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