Generalization of Steffensen's method for operator equations in Banach space
Generalization of the Mercer Theorem
Generalization of the Newman-Shapiro isometry theorem and Toeplitz operators. II
The Newman-Shapiro Isometry Theorem is proved in the case of Segal-Bargmann spaces of entire vector-valued functions (i.e. summable with respect to the Gaussian measure on ℂⁿ). The theorem is applied to find the adjoint of an unbounded Toeplitz operator with φ being an operator-valued exponential polynomial.
Generalization of von Neumann's spectral sets and integral representation of operators
Generalization of Weyl-von Neumann-Berg theorem for the case of normal operator-valued holomorphic functions
Generalizations of Cesàro means and poles of the resolvent
An improvement of the generalization-obtained in a previous article [Bu1] by the author-of the uniform ergodic theorem to poles of arbitrary order is derived. In order to answer two natural questions suggested by this result, two examples are also given. Namely, two bounded linear operators T and A are constructed such that converges uniformly to zero, the sum of the range and the kernel of 1-T being closed, and converges uniformly, the sum of the range of 1-A and the kernel of (1-A)² being...
Generalizations of Kaplansky's Theorem Involving Unbounded Linear Operators
We are mainly concerned with the result of Kaplansky on the composition of two normal operators in the case in which at least one of the operators is unbounded.
Generalizations of Melin's inequality to systems
We discuss a recent necessary and sufficient condition for Melin's inequality for a class of systems of pseudodifferential operators.
Generalizations of Mercer's theorem for a class of nonselfadjoint operators
Generalizations of some classical inequalities and their applications
Generalizations of the Lax-Milgram theorem.
Generalizations of the results on powers of -hyponormal operators.
Generalized -resolvent operator technique and sensitivity analysis for relaxed cocoercive variational inclusions.
Generalized almost-convergence vs. matrix summability
Generalized Analytic and Quasi-Analytic Vectors
For every sequence (aₙ) of positive real numbers and an operator acting in a Banach space, we introduce the families of (aₙ)-analytic and (aₙ)-quasi-analytic vectors. We prove various properties of these families.
Generalized asymptotic pointwise contractions and nonexpansive mappings involving orbits.
Generalized a-Weyl's theorem and the single-valued extension property.
Let T be a bounded linear operator acting on a Banach space X such that T or T* has the single-valued extension property (SVEP). We prove that the spectral mapping theorem holds for the semi-essential approximate point spectrum σSBF-+(T); and we show that generalized a-Browder's theorem holds for f(T) for every analytic function f defined on an open neighbourhood U of σ(T): Moreover, we give a necessary and sufficient condition for such T to obey generalized a-Weyl's theorem. An application is given...
Generalized a-Weyl's theorem for direct sums
Generalized Banach-Mazur distance
Generalized bi-quasi-variational inequalities for quasi-pseudo-monotone type II operators on compact sets
In this paper, the authors prove some existence results of solutions for a new class of generalized bi-quasi-variational inequalities (GBQVI) for quasi-pseudo-monotone type II and strongly quasi-pseudo-monotone type II operators defined on compact sets in locally convex Hausdorff topological vector spaces. In obtaining these results on GBQVI for quasi-pseudo-monotone type II and strongly quasi-pseudo-monotone type II operators, we shall use Chowdhury and Tan’s generalized version [3] of Ky Fan’s...