On the relation of closed forms and Trotter's product formula

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Abstract

The aim of this paper is to give a characterization in Hilbert spaces of the generators of C0-semigroups associated with closed, sectorial forms in terms of the convergence of a generalized Trotter's product formula. In the course of the proof of the main result we also present a similarity result which can be of independent interest: for any unbounded generator A of a C0-semigroup etA it is possible to introduce an equivalent scalar product on the space, such that etA becomes non-quasi-contractive with respect to the new scalar product.

Original languageEnglish
Pages (from-to)401-413
Number of pages13
JournalJournal of Functional Analysis
Volume205
Issue number2
DOIs
Publication statusPublished - Dec 20 2003

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Keywords

  • Closed, sectorial forms
  • Quasi-contractivity
  • Trotter-Kato product formula

ASJC Scopus subject areas

  • Analysis

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