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# Operator-norm approximations of holomorphic one-parameter semigroups of contractions in Hilbert spaces

### Abstract

We establish the operator-norm convergence of the Iosida and Dunford-Segal approximation formulas for one-parameter semigroups of the class $C_0$, gene ated by maximal sectorial generators in separable Hilbert spaces. Our approach is essentially based on the Crouzeix-Delyon theorem [8] related to the generalization of the von Neumann inequality.

### Article Information

 Title Operator-norm approximations of holomorphic one-parameter semigroups of contractions in Hilbert spaces Source Methods Funct. Anal. Topology, Vol. 18 (2012), no. 2, 101-110 MathSciNet MR2978188 zbMATH 1258.47060 Copyright The Author(s) 2012 (CC BY-SA)

### Authors Information

Yury Arlinskiĭ
Department of Mathematical Analysis, East Ukrainian National University, 20-A Kvartal Molodizhny, Lugans'k, 91034, Ukraine

### Citation Example

Yury Arlinskiĭ, Operator-norm approximations of holomorphic one-parameter semigroups of contractions in Hilbert spaces, Methods Funct. Anal. Topology 18 (2012), no. 2, 101-110.

### BibTex

@article {MFAT639,
AUTHOR = {Arlinskiĭ, Yury},
TITLE = {Operator-norm approximations of holomorphic one-parameter semigroups of contractions in Hilbert spaces},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {18},
YEAR = {2012},
NUMBER = {2},
PAGES = {101-110},
ISSN = {1029-3531},
MRNUMBER = {MR2978188},
ZBLNUMBER = {1258.47060},
URL = {http://mfat.imath.kiev.ua/article/?id=639},
}