Abstract
Let {T(t)}(t >= 0) be a C-0-semigroup on a separable Hilbert space H. We show that T(t) is an m-isometry for any t if and only if the mapping t is an element of R+ -> parallel to T(t)x parallel to(2) for each x is an element of H is a polynomial of degree at most m. This property is used to study m-isometric right translation semigroup on weighted L-P-spaces. We also provide alternative characterizations of the above property by imposing conditions on the infinitesimal generator operator and on the cogenerator operator of {T(t)}(t >= 0) Moreover, we prove that a non-unitary 2-isometry T on a Hilbert space satisfying the kernel condition, that is,
T*T(KerT*) subset of KerT*,
can be embedded into a C-0-semigroup if and only if dim(KerT*) = infinity. (C) 2018 Elsevier Inc. All rights reserved.