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Full-Text Articles in Physical Sciences and Mathematics
Weighted Composition Operators Between Vector-Valued Bloch-Type Spaces, Kobra Esmaeili, Hakimeh Mahyar
Weighted Composition Operators Between Vector-Valued Bloch-Type Spaces, Kobra Esmaeili, Hakimeh Mahyar
Turkish Journal of Mathematics
Let $X$ and $Y$ be complex Banach spaces and $\mathbb{D}$ be the open unit disc in the complex plane $\mathbb{C}$. Let $\varphi$ be an analytic self-map of $\mathbb{D}$ and $\psi$ be an analytic operator-valued function from $\mathbb{D}$ into the space of all bounded linear operators from $X$ to $Y.$ The weighted composition operator $W_{\psi,\varphi}:\mathcal{H} \rightarrow\mathcal{H}(\mathbb{D}, Y)$ is defined by $$ W_{\psi,\varphi}( f)(z)=\psi(z)(f(\varphi(z))), \quad \quad (z\in\mathbb{D}, f\in \mathcal{H}),$$ where $\mathcal{H}$ is the space of all analytic $X$-valued functions on $\mathbb{D}$. In this paper we provide necessary and sufficient conditions for the boundedness and compactness of weighted composition operators $W_{\psi,\varphi}$ between vector-valued …
On A Theorem Of Terzioğlu, Asuman Güven Aksoy
On A Theorem Of Terzioğlu, Asuman Güven Aksoy
Turkish Journal of Mathematics
The theory of compact linear operators acting on a Banach space has a classical core and is familiar to many. Perhaps less known is the characterization theorem of Terzioğlu for compact maps. This theorem has a number of important connections that deserves illumination. In this paper we survey Terzioğlu's characterization theorem for compact maps and some of its consequences. We also prove a similar characterization theorem for $Q$-compact maps.