Powers of Class $p$-$wA(s,t)$ Operators Associated with Generalized Aluthge Transformations (European Journal of Pure and Applied Mathematics, 2026)
Let $T = U|T|$ be a polar decomposition of a bounded linear operator $T$ on a complex Hilbert space with $\ker U = \ker |T|$. $T$ is said to be class $p$-$wA(s,t)$ if\[\left( |T^{*}|^{t} |T|^{2s} |T^{*}|^{t} \right)^{\frac{tp}{s+t}} \geq |T^{*}|^{2tp}\quad\text{and}\quad|T|^{2sp} \geq \left( |T|^{s} |T^{*}|^{2t} |T|^{s} \right)^{\frac{sp}{s+t}}\]with $0 < p \leq 1$ and $0 < s, t, s + t \leq 1$.This is a generalization of $p$-hyponormal or class $A$ operators. In this paper, we shall show that if $T$ belongs to class $p$-$wA(s,t)$ operator for $0
Keywords: class $p$-$wA(s,t)$; normaloid; isoloid