A condition equivalent to uniform ergodicity
Let T be a linear operator on a Banach space X with for some 0 ≤ w < 1. We show that the following conditions are equivalent: (i) converges uniformly; (ii) .
A connection between spectral radius and trace
A constructive proof of the composition rule for Taylor's functional calculus
We give a new constructive proof of the composition rule for Taylor's functional calculus for commuting operators on a Banach space.
A continuation theorem for holomorphic mapping into a Hilbert space
A convergence result for discrete steepest descent in weighted Sobolev spaces.
A convergence theorem for Dirichlet forms with applications to boundary value problems with varying domains.
A Convergence Theorem for Selfadjoint Operators Applicable to Dirac Operators with Cutoff Potentials.
A convex treatment of numerical radius inequalities
We prove an inner product inequality for Hilbert space operators. This inequality will be utilized to present a general numerical radius inequality using convex functions. Applications of the new results include obtaining new forms that generalize and extend some well known results in the literature, with an application to the newly defined generalized numerical radius. We emphasize that the approach followed in this article is different from the approaches used in the literature to obtain such...
A counterexample to a compact embedding theorem for functions with values in a Hilbert space.
A counterexample to the Γ-interpolation conjecture
Agler, Lykova and Young introduced a sequence , where ν ≥ 0, of necessary conditions for the solvability of the finite interpolation problem for analytic functions from the open unit disc into the symmetrized bidisc Γ. They conjectured that condition is necessary and sufficient for the solvability of an n-point interpolation problem. The aim of this article is to give a counterexample to that conjecture.
A decoupling approach to resonances for multiparticle quantum scattering systems
A density theorem for algebra representations on the space (s)
We show that an arbitrary irreducible representation T of a real or complex algebra on the F-space (s), or, more generally, on an arbitrary infinite (topological) product of the field of scalars, is totally irreducible, provided its commutant is trivial. This provides an affirmative solution to a problem of Fell and Doran for representations on these spaces.
A dilation theorem for operators on Banach spaces
A discrepancy principle for Tikhonov regularization with approximately specified data
Many discrepancy principles are known for choosing the parameter α in the regularized operator equation , , in order to approximate the minimal norm least-squares solution of the operator equation Tx = y. We consider a class of discrepancy principles for choosing the regularization parameter when T*T and are approximated by Aₙ and respectively with Aₙ not necessarily self-adjoint. This procedure generalizes the work of Engl and Neubauer (1985), and particular cases of the results are applicable...
A discrete Hardy-Laptev-Weidl-type inequality and associated Schrödinger-type operators.
A finite multiplicity Helson-Lowdenslager-de Branges theorem
We prove two theorems. The first theorem reduces to a scalar situation the well known vector-valued generalization of the Helson-Lowdenslager theorem that characterizes the invariant subspaces of the operator of multiplication by the coordinate function z on the vector-valued Lebesgue space L²(;ℂⁿ). Our approach allows us to prove an equivalent version of the vector-valued Helson-Lowdenslager theorem in a completely scalar setting, thereby eliminating the use of range functions and partial isometries....
A fixed point theorem for affine mappings and its application to elasticity theory
In this paper we obtain a general fixed point theorem for an affine mapping in Banach space. As an application of this theorem we study existence of periodic solutions to the equations of the linear elasticity theory.
A formula for the eigenvalues of a compact operator
A formula for the inner spectral radius.
A formula to calculate the spectral radius of a compact linear operator.