On the Wiener-Eberlein theorem
On the “zero-two” law for positive contractions in the Banach-Kantorovich lattice
In the present paper we prove the “zero-two” law for positive contractions in the Banach-Kantorovich lattices , constructed by a measure with values in the ring of all measurable functions.
On torsional rigidity and principal frequencies: an invitation to the Kohler−Jobin rearrangement technique
We generalize to the p-Laplacian Δp a spectral inequality proved by M.-T. Kohler−Jobin. As a particular case of such a generalization, we obtain a sharp lower bound on the first Dirichlet eigenvalue of Δp of a set in terms of its p-torsional rigidity. The result is valid in every space dimension, for every 1 < p < ∞ and for every open set with finite measure. Moreover, it holds by replacing the first eigenvalue with more general optimal Poincaré-Sobolev constants. The method of proof...
On totally -paranormal operators
In this paper we study some properties of a totally -paranormal operator (defined below) on Hilbert space. In particular, we characterize a totally -paranormal operator. Also we show that Weyl’s theorem and the spectral mapping theorem hold for totally -paranormal operators through the local spectral theory. Finally, we show that every totally -paranormal operator satisfies an analogue of the single valued extension property for and some of totally -paranormal operators have scalar extensions....
On transitive systems of subspaces in a Hilbert space.
On triangularization of algebras of operators.
On two-sided interpolation for upper triangular matrices.
On typical Markov operators acting on Borel measures.
On uniformly smoothing stochastic operators
We show that a stochastic operator acting on the Banach lattice of all -integrable functions on is quasi-compact if and only if it is uniformly smoothing (see the definition below).
On uniqueness in electromagnetic scattering from biperiodic structures
Consider time-harmonic electromagnetic wave scattering from a biperiodic dielectric structure mounted on a perfectly conducting plate in three dimensions. Given that uniqueness of solution holds, existence of solution follows from a well-known Fredholm framework for the variational formulation of the problem in a suitable Sobolev space. In this paper, we derive a Rellich identity for a solution to this variational problem under suitable smoothness conditions on the material parameter. Under additional...
On unitary equivalence of invariant subspaces of the Dirichlet space
It is shown that in the Dirichlet space , two invariant subspaces ℳ ₁, ℳ ₂ of the Dirichlet shift are unitarily equivalent only if ℳ ₁ = ℳ ₂.
On unrestricted products of (W) contractions
Given a family of (W) contractions on a reflexive Banach space X we discuss unrestricted sequences . We show that they converge weakly to a common fixed point, which depends only on x and not on the order of the operators if and only if the weak operator closed semigroups generated by are right amenable.
On upper and lower bounds of the numerical radius and an equality condition
We give an inequality relating the operator norm of T and the numerical radii of T and its Aluthge transform. It is a more precise estimate of the numerical radius than Kittaneh's result [Studia Math. 158 (2003)]. Then we obtain an equivalent condition for the numerical radius to be equal to half the operator norm.
On von Neumann's inequality.
On Weak Convergence of Norm Preserving Operators on L2 (X) and its Application to Measure Preserving Transformations.
On weak (r,2)-summing operators and weak Hilbert spaces
On weak supercyclicity II
This paper considers weak supercyclicity for bounded linear operators on a normed space. On the one hand, weak supercyclicity is investigated for classes of Hilbert-space operators: (i) self-adjoint operators are not weakly supercyclic, (ii) diagonalizable operators are not weakly -sequentially supercyclic, and (iii) weak -sequential supercyclicity is preserved between a unitary operator and its adjoint. On the other hand, weak supercyclicity is investigated for classes of normed-space operators:...
On w-hyponormal operators
We study some properties of w-hyponormal operators. In particular we show that some w-hyponormal operators are subscalar. Also we state some theorems on invariant subspaces of w-hyponormal operators.
On λ-commuting operators
For a scalar λ, two operators T and S are said to λ-commute if TS = λST. In this note we explore the pervasiveness of the operators that λ-commute with a compact operator by characterizing the closure and the interior of the set of operators with this property.
Once more about the monotonicity of the Temple quotients
A new proof of the monotonicity of the Temple quotients for the computation of the dominant eigenvalue of a bounded linear normal operator in a Hilbert space is given. Another goal of the paper is a precise analysis of the length of the interval for admissible shifts for the Temple quotients.