# The Cayley transform of the generator of a bounded C0-semigroup

A. Gomilko, Heiko J. Zwart

5 Citations (Scopus)

## Abstract

Let $A$ be the generator of a uniformly bounded $C_0$-semigroup on the Banach space $X$. We present sufficient conditions on the resolvent $(A-\lambda I)^{-1},$ $Re(\lambda)>0,$ under which the Cayley transform $V=(A+I)(A-I)^{-1}$ is a power-bounded operator, i.e., $\sup_{n\in N}\,\|V^n\|\,<\infty.$
Original language Undefined 10.1007/s00233-006-0648-8 140-148 9 Semigroup forum 74 1/1 https://doi.org/10.1007/s00233-006-0648-8 Published - Feb 2007

## Keywords

• MSC-93C25
• IR-63698
• EWI-8191
• METIS-241701