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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.


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Article Information

TitleOperator-norm approximations of holomorphic one-parameter semigroups of contractions in Hilbert spaces
SourceMethods Funct. Anal. Topology, Vol. 18 (2012), no. 2, 101-110
MathSciNet MR2978188
zbMATH 1258.47060
CopyrightThe 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 


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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},
}


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