Weighted Inequalities for Quasi-Monotone Functions

The purpose of this paper is to give characterizations of weightsfor which reverse inequalities of Hölder type for quasi-monotonefunctions are satisfied. Our inequalities with general weightsand with sharp constants complement the results of [2, 8, 9]and [16, 17] for the values of parameters p and q with 1pq<.     

Properties of Certain Integral Operators

For analytic functions f() belonging to the class A_p, integral operators I_n^a (f()) are introduced. The object of the present paper is to derive some interesting properties of integral operators I_n^a(f(z)). Our results contain some previous results by M. Obradovié [4], S. Owa, M. Obradovi, and M. Nunokawa [6], and by D.K. Thomas [7].AMS Subject Classification (2000) primary 30C45 secondary 32A20Supported, in part, by the Japanese Ministry of Education, Science and Culture under a grant-in-aid for general scientific research.     

可分解算子的某些性质

In this paper, we have proved the following two theorems: Theorem1. If T⁽⁴⁾∈SVEP, then τX is an analytic invariant subspace of T⁽²⁾, where τ is the natural imbedding from X to X⁽²⁾.Theorem 2. If T⁽¹⁾ is decomposable, then T is decomposable too.The authois take this opportunity to express their gratitude to the author of [2].     

p-ω-亚正规算子的一些性质

In this paper,let T be a bounded linear operator on a complex Hilbert H.We give and prove that every p-w-hyponormal operator has Bishop's property(β)and spectral properties;Quasi-similar p-w-hyponormal operators have equal spectra and equal essential spectra.Finally,for p-w-hyponormal operators,we give a kind of proof of its normality by use of properties of partial isometry.     

Approximation Properties by q-Durrmeyer-Stancu Operators

In this paper, we are dealing with q-Bemstein-Durrmeyer-Stancu operators. Firstly, we have estimated moments of these operators. Then we have discussed some approximation properties and asymptotic formulas. We have obtained better estimations by using King type approach and given statistical convergence for the operators.     

Properties of a Family of Operators

In this paper we define a family of new nonsymmetric operators of generalized translation and describe their properties. For each of these operators, we introduce a generalized modulus of smoothness, for which the direct and inverse theorems of approximation theory are given.     

Integrability Properties of Maximal Convolution Operators

In this article we study integrability properties of maximal convolution operators satisfying restricted weak type (p, p) estimates.     

Algebraic Properties of Generalized Toeplitz Operators

§ 1.Introduction　 Let D be the unit disk of the complex plane C,T the unit circle,and H2 the Hardyspace of the unit circle.For operators on H2 ,all matrices in the sequel will be formedwith respect to the basis { e0 ,e1 ,… } defined by en(z) =zn,n=0 ,1 ,2 ,… . Ifφ∈ L∞ (T) ,write Tφfor the corresponding Toeplitz operator defined on H2 by Tφf=P(φf) (where Pis the projection from L2 (T) onto H2 ) .The Toeplitz operator Te1,the so called unilat-eral shift,will be denoted by U thr…     

Approximation Properties of Two-Dimensional q-Bernstein-Chlodowsky-Durrmeyer Operators

This article deals with the Durrmeyer-type generalization of the q-Bernstein-Chlodowsky operators on a rectangular domain (which were introduced by Büyükyaz?c? [2 ?. Büyükyaz?c? ( 2009 ). On the approximation properties of two-dimensional q-Bernstein-Chlodowsky polynomials . Math. Commun. 14 : 255 – 269 .[Web of Science ®] , [Google Scholar]]). We obtain the Korovkin-type approximation properties and the rates of convergence of this generalization using the means of the modulus of continuity and using the K-functional of Peetre. Further, we establish the weighted approximation properties for these operators.     

Smoothness Properties of Modified Bernstein-Kantorovich Operators

In this article, we consider modified Bernstein-Kantorovich operators and investigate their approximation properties. We show that the order of approximation to a function by these operators is at least as good as that of ones classically used. We obtain a simultaneous approximation result for our operators. Also, we prove two direct approximation results via the usual second-order modulus of smoothness and the second-order Ditzian-Totik modulus of smoothness, respectively. Finally, some graphical illustrations are provided.     

B-Fredholm Properties of Closed Invertible Operators

In this paper, we study B-Fredholm spectral properties of an invertible closed linear operator in relation with the B-Fredholm spectral properties of its bounded inverse. Precisely, for such operator, we characterize its B-Fredholm spectrum and other related spectra in terms of the corresponding spectra of its bounded inverse. As an application, we show that every normal operator with nonempty resolvent set, in particular self-adjoint Schrödinger operators, satisfies generalized Weyl’s theorem.

     

完全超约化算子的几个性质

本文讨论了完全超约化算子的性质，共得到三个结果，主要结果是给出了完全超约化算子有一个超约的特征向量的充分条件。     

Approximation Properties For Modified q-Bernstein-Kantorovich Operators

The purpose of this article is to give a generalization of q-Bernstein-Kantorovich operators. We present some approximation theorems. We compute the rate of convergence and error estimation of these operators by means of the modulus of continuity. Furthermore, we give some numerical examples to show comparisons in illustrative graphics for the convergence of these operators to various functions.     

Approximation Properties and Some Classes of Operators

The following questions and close problems are studied.(i) Is it true that T is p-nuclear provided that T ^** is p-nuclear? (ii) Is it true that Tis dually p-nuclear provided that T ^* is p-nuclear? (iii) Is it true that if T ^*is compactly factorable in the space l _p, then T is (strictly) factorable in the space l _p'? Here, T ^* is the adjoint operator of a bounded operator T:X Yin Banach spaces X and Y. Bibliography: 30 titles.     

On Applications of Quasi-Monotone Sequences and Quasi Power Increasing Sequences

In this article, we prove a general theorem dealing with an application of quasi-f-power increasing sequences and δ-quasi monotone sequences. This theorem also includes some known and new results.     

Spectral Inclusion Properties of Unbounded Hamiltonian Operators

In this paper, the authors investigate the spectral inclusion properties of the quadratic numerical range for unbounded Hamiltonian operators. Moreover, some examples are presented to illustrate the main results.     

模糊粗糙近似算子的拓扑性质

考虑论域上一二元关系所决定的模糊粗糙近似算子的拓扑性质,证明了任一自反二元关系可以决定一模糊拓扑.并且,当二元关系自反对称时,该模糊拓扑中的元是开集当且仅当它是闭集;当二元关系自反传递时,该模糊拓扑的闭包与内部算子恰为模糊粗糙上、下近似算子.