Recall that the Lorentz ideal C− p is the collection of operators A satisfying the condition ‖A‖p = ∑∞ j=1 j sj(A) < ∞. Consider Hankel operators Hf : H(S) → L(S, dσ) H(S), where H(S) is the Hardy space on the unit sphere S in C. In this paper we characterize the membership Hf ∈ C− p , 2n < p <∞.

The paper continues the study of differential Banach *algebras AS and FS of operators associated with symmetric operators S on Hilbert spaces H. The algebra AS is the domain of the largest *-derivation δS of B(H) implemented by S and the algebra FS is the closure of the set of all finite rank operators in AS with respect to the norm ‖A‖ = ‖A‖+‖δS(A)‖. When S is selfadjoint, FS is the domain of ...

Keywords: q-Bernstein–Schurer–Stancu operators q-integers Modulus of smoothness Rate of convergence a b s t r a c t In the present paper, we introduce the Stancu type generalization of the Bernstein–Schurer operators based on q integers. First, we prove the basic convergence of S ða;bÞ n;p ð:; q; xÞ and then obtain the rate of convergence by these operators in terms of the modulus of continuity...

A bounded linear operator between Banach spaces is called completely continuous if it carries weakly convergent sequences into norm convergent sequences. Isolated is a universal operator for the class of non-completely-continuous operators from L1 into an arbitrary Banach space, namely, the operator from L1 into `∞ defined by T0(f) = Z rnf dμ n≥0 , where rn is the nth Rademacher function. It is...

First of all, in this paper we propose a family of fuzzy implication operators, which the generalised Luckasiewicz ́s one, and to analyse the impacts of Smets and Magrez properties on these operators. The result of this approach will be a characterisation of a proposed family of inclusion grade operators (in Bandler and Kohout ́s manner) that satisfies the axioms of Divyendu and Dogherty. Second,...

In this talk I will give a overview on the connections between closure operators and choice operators and on related results. An operator on a finite set S is a map defined on the set P(S) of all the subsets of S. A closure operator is an extensive, isotone and idempotent operator. A choice operator c is a contracting operator (c(A) ⊆ A, for every A ⊆ S). Choice operators and their lattices hav...

The aim of this text is the study of the fine spectra for a class of Cesàro generalized operators, Rhaly operators, when those are defined on the spaces lp, p > 1. 2000 Mathematical Subject Classification: 65F15 The averaging operators A are determined by relations inf x∈X f(x) ≤ A(f) ≤ sup x∈X f(x) , ∀ f ∈ F = {f | f : X → R}, where ∅ 6= X ⊂ R. A(f) is the mean of f for the operator A. For a =...

The main purpose of this note is to characterize the operators S ∈ ker∆A,B ∩ C1 which are orthogonal to the range of elementary operators, where S is not a smooth point in C1 by using the φ−directional derivative.

The Teichmüller space Teich(S) of a surface S in genus g > 1 is a totally real submanifold of the quasifuchsian space QF(S). We show that the determinant of the Laplacian det′(∆) on Teich(S) has a unique holomorphic extension to QF(S). To realize this holomorphic extension as the determinant of differential operators on S, we introduce a holomorphic family {∆μ,ν} of elliptic second order differ...

In this note we study the structure of shift-preserving operators acting on a finitely generated shift-invariant space. We define new notion diagonalization for these operators, which call s-diagonalization. give necessary and sufficient conditions bounded operator in order to be s-diagonalizable. These are terms its range operator. also obtain generalized Spectral Theorem normal operators.