A minimum modulus theorem and applications to ultradifferential operators

A Fixed Point Theorem for Sum of Operators and Applications

In the present paper we establish a fixed point result of Krasnoselskii type for the sum A+B, where A and B are sequentially weakly continuous, and B is a nonexpansive mapping. As an application, we study the existence of solutions for an nonlinear integral equation in Banach spaces. In the last section we develop a sequentially weak continuity result for a class of operators acting on vector-v...

Spectral Theorem for Normal Operators: Applications

In these notes, we present a number of interesting and diverse applications of the Spectral Theorem for Normal Operators. These include a Spectral Mapping Theorem for Normals Operators, a Spectral Characterization of Algebraic Operators, von Neumann’s Mean Ergodic Theorem, Pathconnectivity of the Group of Invertible Operators, and some Polynomial Approximation Results for Operators.

A T(1)-Theorem in relation to a semigroup of operators and applications to new paraproducts

On genuine Lupac{s}-Beta operators and modulus of continuity

In the present article we discuss approximation properties of genuine Lupac{s}-Beta operators of  integral type. We establish quantitative asymptotic formulae and a direct estimate in terms of Ditzian-Totik modulus of continuity. Finally we mention  results on the weighted modulus of continuity for the genuine operators.

A generalized Weyl equidistribution theorem for operators with applications

The present paper is motivated by the observation that Weyl's equidistribution theorem for real sequences on a bounded interval can be formulated in a way which is also meaningful for sequences of self-adjoint operators on a hilbert space. We shall provide general results on weak convergence of operator measures which yield this version of Weyl's theorem as a corollary. Further, by combining th...