Poisson's equation and characterizations of reflexivity of Banach spaces

Vladimir P. Fonf, Michael Lin, Przemysław Wojtaszczyk
2011 Colloquium Mathematicum  
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 obtain that X (with a basis) is reflexive if and only if every strongly continuous bounded semi-group {T t : t ≥ 0} with generator A satisfies The range (I − T )X (respectively, AX for continuous time) is the space of x ∈ X for which Poisson's equation (I − T )y = x (Ay = x in continuous time) has a solution y ∈ X; the above equalities for
more » ... he ranges express sufficent (and obviously necessary) conditions for solvability of Poisson's equation.
doi:10.4064/cm124-2-7 fatcat:gfph6q6lbbfx3p4aqb6x3bjpea