Displaying similar documents to “A note on the powers of Cesàro bounded operators”

On discreteness of spectrum of a functional differential operator

Sergey Labovskiy, Mário Frengue Getimane (2014)

Mathematica Bohemica

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We study conditions of discreteness of spectrum of the functional-differential operator ℒ u = - u ' ' + p ( x ) u ( x ) + ∫ - ∞ ∞ ( u ( x ) - u ( s ) ) d s r ( x , s ) on ( - ∞ , ∞ ) . In the absence of the integral term this operator is a one-dimensional Schrödinger operator. In this paper we consider a symmetric operator with real spectrum. Conditions of discreteness are obtained in terms of the first eigenvalue of a truncated operator. We also obtain one simple condition for discreteness of spectrum.

Boundedness properties of resolvents and semigroups of operators

J. van Casteren (1997)

Banach Center Publications

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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 ) ∑ j = 0 n ∥ T j x ∥ 2 ≤ 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 ∈ ℕ is finite. In fact the following inequality is valid for all n ∈ ℕ: ∥Tn∥ ≤ e M(T)M(T*)....

On Kurzweil-Henstock equiintegrable sequences

Štefan Schwabik, Ivo Vrkoč (1996)

Mathematica Bohemica

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For the Kurzweil-Henstock integral the equiintegrability of a pointwise convergent sequence of integrable functions implies the integrability of the limit function and the relation m abfm(s)s = abm fm(s)s. Conditions for the equiintegrability of a sequence of functions pointwise convergent to an integrable function are presented. These conditions are given in terms of convergence of some sequences of integrals.