On an extension of operator transforms

We introduce the $λ$-mean transform $M_λ(T)$ of a Hilbert space operator $T$ as an extension of some operator transforms based on the Duggal transform $T^D$ by $M_λ(T) := λT + (1-λ)T^D$, and present some of its essentially properties. Among other things, we obtain estimates for the operator norm and numerical radius of the $λ$-mean transform $M_λ(T)$ in terms of the original operator $T$.

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