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

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

2006-11-30

arxiv.org/abs/math/0611933v1

J. Funct. Anal. 205 (2003), no. 2, 401--413

Mathematics

Functional Analysis

12 pages

Scientific paper

The aim of this paper is to give a characterization in Hilbert spaces of the generators of $C_0$-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 $C_0$-semigroup $e^{tA}$ it is possible to introduce an equivalent scalar product on the space, such that $e^{tA}$ becomes non-quasi-contractive with respect to the new scalar product.

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