REMARKS ON l1 AND l∞-MAXIMAL REGULARITY FOR POWER-BOUNDED OPERATORS

We discuss l(p)-maximal regularity of power-bounded operators and relate the discrete to the continuous time problem for analytic semigroups. We give a complete characterization of operators with l(1), and l(infinity)-maximal regularity. We also introduce an unconditional form of Ritt's condition for power-bounded operators, which plays the role of the existence of an H-infinity-calculus, and give a complete characterization of this condition in the case of Banach spaces which are L-1-spaces, C(K)-spaces or Hilbert spaces.