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Currently displaying 1 – 3 of 3

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Approximation properties and universal Banach spaces

Przemyslaw Wojtaszczyk — 1972

Mémoires de la Société Mathématique de France

On separable Banach spaces containing all separable reflexive Banach spaces

Przemysław Wojtaszczyk — 1971

Studia Mathematica

Poisson's equation and characterizations of reflexivity of Banach spaces

Vladimir P. Fonf; Michael Lin; Przemysław Wojtaszczyk — 2011

Colloquium Mathematicae

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 $x \in X : s u p_{n} | | \sum_{k = 1}^{n} T^{k} x | | < \infty$ = (I-T)X $.$ We then deduce that X (with a basis) is reflexive if and only if every strongly continuous bounded semigroup $T_{t} : t \geq 0$ with generator A satisfies $A X = x \in X : s u p_{s > 0} | | \int_{0}^{s} T_{t} x d t | | < \infty$ . 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 the ranges...

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