Poisson's equation and characterizations of reflexivity of banach spaces

Vladimir P. Fonf, Michael Lin, Przemysław Wojtaszczyk

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

Let X be a Banach space with a basis. We prove that X is reflexive if and only if every power-bounded linear operator T satisfies Browder's equality We then deduce that X (with a basis) is reflexive if and only if every strongly continuous bounded semigroup {Tt: t ≥ 0} with generator A satisfies The range (I - T)X (respectively, AX for continuous time) is the space of x ε X for which Poisson's equation (I-T)y = x (Ay = x in continuous time) has a solution y ε X; the above equalities for the ranges express sufficient (and obviously necessary) conditions for solvability of Poisson's equation.

Original languageEnglish
Pages (from-to)225-235
Number of pages11
JournalColloquium Mathematicum
Volume124
Issue number2
DOIs
StatePublished - 1 Dec 2011

Keywords

  • Mean ergodic operator
  • Power-bounded operator
  • Reflexive Banach space

ASJC Scopus subject areas

  • Mathematics (all)

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