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REMARKS ON ℓ1 AND
-MAXIMAL REGULARITY FOR POWER-BOUNDED OPERATORS
- Part of
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- Journal:
- Journal of the Australian Mathematical Society / Volume 84 / Issue 3 / June 2008
- Published online by Cambridge University Press:
- 01 June 2008, pp. 345-365
- Print publication:
- June 2008
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- Article
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We discuss ℓp-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 ℓ1 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.
-MAXIMAL REGULARITY FOR POWER-BOUNDED OPERATORS
-calculus, and give a complete characterization of this condition in the case of Banach spaces which are 