HIGHER ORDER EXPONENTIALLY ISOMETRIC OPERATORS

HIGHER ORDER EXPONENTIALLY ISOMETRIC OPERATORS

For a positive integer m, a bounded linear operator T on a Hilbert space is called an exponentially m-isometric operator if mP k=0 (????1)m????k????m k ekT ekT = 0. We show that for every non-empty com- pact subset K of pure imaginary axis, there exits an exponentially m- isometric operator T whose spectrum is K. Moreover, if (Tn)n 1 is a sequence of operators in this class that converges to T in the strong operator topology, then T is also an exponentially m-isometric operator.