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

Matolcsi, Máté (2003) On the relation of closed forms and Trotter's product formula. JOURNAL OF FUNCTIONAL ANALYSIS, 205 (2). pp. 401-413. ISSN 0022-1236

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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.

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