A Convergence Theorem for Selfadjoint Operators Applicable to Dirac Operators with Cutoff Potentials.
A convergent nonlinear splitting via orthogonal projection
We study the convergence of the iterations in a Hilbert space , where maps into itself and is a linear projection operator. The iterations converge to the unique fixed point of , if the operator is continuous and the Lipschitz constant . If an operator satisfies these assumptions and is an orthogonal projection such that , then the operator is defined and continuous in and satisfies .
A converse to the Lions-Stampacchia theorem
In this paper we show that a linear variational inequality over an infinite dimensional real Hilbert space admits solutions for every nonempty bounded closed and convex set, if and only if the linear operator involved in the variational inequality is pseudo-monotone in the sense of Brezis.
A converse to the Lions-Stampacchia Theorem
In this paper we show that a linear variational inequality over an infinite dimensional real Hilbert space admits solutions for every nonempty bounded closed and convex set, if and only if the linear operator involved in the variational inequality is pseudo-monotone in the sense of Brezis.
A convex operator function.
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 counter example on common periodic points of functions.
A counterexample in operator theory
The purpose of this note is to give an explicit construction of a bounded operator T acting on the space L2[0,1] such that |Tf(x)| ≤ ∫01 |f(y)| dy for a.e. x ∈ [0.1], and, nevertheless, ||T||Sp = ∞ for every p < 2. Here || ||Sp denotes the norm associated to the Schatten-Von Neumann classes.
A counterexample to a compact embedding theorem for functions with values in a Hilbert space.
A counterexample to a theorem of Argyros
A counterexample to “An extension of Gregus fixed point theorem”.
A counterexample to the article “On the fixed points of affine nonexpansive mappings”.
A counterexample to the L² estimate //Xyu//...C(//X...u// + //Y...u// + //u//).
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 Criterion for an Operator with Real Spectrum to Be of Scalar-type.
A criterion for compositions of (p,q)-absolutely summing operators to be compact
A criterion for discrete spectra of partial differential operators
A criterium for the strict positivity of the density of the law of a Poisson process.
A decoupling approach to resonances for multiparticle quantum scattering systems
A degree for a class of acyclic-valued vector fields in Banach spaces