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- W393458201 abstract "The purpose of this paper is to establish some properties of $rho$-oid operators and to extend the class of operators satisfying the growth $condition-(G_{1})$ by considering the growth condition upon the operator radius of the resolvent of an operator. For an operator (a bounded linear transformation) $T$ on a camplex Hilbert space $H$, let $sigma(T),$ $overline{W(T)},$ $r(T)$ and $|W(T)|$ denote $re8pectively$ , the spectrum, the closure of the numerical range $W(T)$ , the spectral radius and the numerical radius of $T$. If $S$ is a set of complex numbers then we write $partial S$ and $con(S)$ for the boundary and the convex hull of $S$ . Let $C_{rho}(rho>0)$ be the class of operators $T$ on $H$ for which there exists a Hilbert space $K$ containing $H$ as a subspace and a unitary operator $U$ on $K$ 8atisfying the following relation: $T^{n}x=rho PU^{n}x(n=1,2,3, cdots)$ , $xeH$ ." @default.
- W393458201 created "2016-06-24" @default.
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- W393458201 date "1976-01-01" @default.
- W393458201 modified "2023-09-28" @default.
- W393458201 title "ON SOME CLASSES OF OPERATORS ASSOCIATED WITH OPERATOR RADII OF HOLBROOK" @default.
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