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Boundedness properties of resolvents and semigroups of operators

J. van Casteren — 1997

Banach Center Publications

Let T: H → H be an operator in the complex Hilbert space H. Suppose that T is square bounded in average in the sense that there exists a constant M(T) with the property that, for all natural numbers n and for all x ∈ H, the inequality $1 / (n + 1) \sum_{j = 0}^{n} ∥ T^{j} x ∥^{2} \leq M {(T)}^{2} ∥ x ∥^{2}$ is satisfied. Also suppose that the adjoint T* of the operator T is square bounded in average with constant M(T*). Then the operator T is power bounded in the sense that $s u p ∥ T^{i} n ∥ : n \in ℕ$ is finite. In fact the following inequality is valid for all n ∈ ℕ: ∥Tn∥ ≤ e M(T)M(T*). Suppose...

The conjugate of the product of operators

J. van Casteren; Seymour Goldberg — 1970

Studia Mathematica

On differences of heat semigroups

J. A. Van Casteren; M. Demuth — 1989

Annales scientifiques de l'Université de Clermont-Ferrand 2. Série Probabilités et applications

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