On an extension of operator transforms

Abstract

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

It is submitted on 26 Feb 2020 to a research journal