Complex symmetric C0-semigroups on the Fock space

Abstract

Please cite this article in press as: P.V. Hai, L.H. Khoi, Complex symmetric C 0 -semigroups on the Fock space, J. Math. Anal. Appl. (2016), http://dx.Abstract. In this paper we introduce a new concept in dynamical systems: the complex symmetric operator C 0 -semigroups (groups) acting on Hilbert space. Using techniques of weighted composition operators we study these semigroups on the Fock space F 2 and show, in particular, that complex symmetric operator C 0 -semigroups contain the familiar unitary semigroups as a proper subclass.