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REMARKS ON 1 AND -MAXIMAL REGULARITY FOR POWER-BOUNDED OPERATORS

Published online by Cambridge University Press:  01 June 2008

N. J. KALTON
Affiliation:
Department of Mathematics, University of Missouri–Columbia, Columbia, MO 65211, USA (email: [email protected])
P. PORTAL*
Affiliation:
Centre for Mathematics and its Applications, Australian National University, Canberra, ACT 0200, Australia (email: [email protected])
*
For correspondence; e-mail: [email protected]
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Abstract

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We discuss 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 1 and -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 -calculus, and give a complete characterization of this condition in the case of Banach spaces which are L1-spaces, C(K)-spaces or Hilbert spaces.

Type
Research Article
Copyright
Copyright © 2008 Australian Mathematical Society

Footnotes

The first author acknowledges support from NSF grant DMS-0244515.

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