Exponentially m-isometric operators on Hilbert spaces

For a positive integer m, a bounded linear operator T on a Hilbert space is called an exponentially m -isometric operator if Sigma(m)(k =0) (-1)(m-k)((k) (m))e(kT)* e(kT) = 0. For 1 <= n <= m, skew-n-selfadjoint operators, nilpotent operators of order less than or equal to [m+1/2], the greatest integer not greater than [m+1/2], and 2 pi i multiples of idempotents 2 are main examples of such operators. We establish a decomposition theorem for strict exponentially m -isometric operators with finite spectrum and prove that they are exponentially isometric m -Jordan. Finally, the dynamics of this operator will be considered. We will show that there is no N-supercyclic exponentially m-isometric operator on an infinite-dimensional Hilbert space.(c) 2023 Elsevier Inc. All rights reserved. [