Year: 2019
Type: article
Abstract: It is known that a $$C_0$$ -semigroup of Hilbert space operators is m-isometric if and only if its generator satisfies a certain condition, which we choose to call m-skew-symmetry. This paper contains two main results: We provide a Lumer–Phillips type characterization of generators of m-isometric semigroups. This is based on the simple observation that m-isometric semigroups are quasicontractive. We also characterize cogenerators of 2-isometric semigroups. To this end, our main strategy is to construct a functional model for 2-isometric semigroups with analytic cogenerators. The functional model yields numerous simple examples of non-unitary 2-isometric semigroups, but also allows for the construction of a closed, densely defined, 2-skew-symmetric operator which is not a semigroup generator.
Author: Eskil Rydhe
Institution: University of Leeds
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,690
Award: G5243045963
OpenAlex ID: W2944844905