Weyl Type Theorems for Left and Right Polaroid Operators

A bounded operator defined on a Banach space is said to be polaroid if every isolated point of the spectrum is a pole of the resolvent. In this paper we consider the two related notions of left and right polaroid, and explore them together with the condition of being a-polaroid. Moreover, the equivalences of Weyl type theorems and generalized Weyl type theorems are investigated for left and a-polaroid operators. As a consequence, we obtain a general framework which allows us to derive in a unified way many recent results, concerning Weyl type theorems (generalized or not) for important classes of operators.     

A Unifying Approach to Weyl Type Theorems for Banach Space Operators

Weyl type theorems have been proved for a considerably large number of classes of operators. In this paper, by introducing the class of quasi totally hereditarily normaloid operators, we obtain a theoretical and general framework from which Weyl type theorems may be promptly established for many of these classes of operators. This framework also entails Weyl type theorems for perturbations f(T + K), where K is algebraic and commutes with T, and f is an analytic function, defined on an open neighborhood of the spectrum of T + K, such that f is non constant on each of the components of its domain.     

SVEP and Generalized Weyl’s Theorem

We use localised single-valued extension property to prove generalized Weyl/Browder and a-generalized Weyl/Browder type theorems for Banach space operators.     

Existence and Liouville theorems for V -harmonic maps from complete manifolds

We establish existence and uniqueness theorems for V-harmonic maps from complete noncompact manifolds. This class of maps includes Hermitian harmonic maps, Weyl harmonic maps, affine harmonic maps, and Finsler harmonic maps from a Finsler manifold into a Riemannian manifold. We also obtain a Liouville type theorem for V-harmonic maps. In addition, we prove a V-Laplacian comparison theorem under the Bakry-Emery Ricci condition.     

The Local Spectral Properties of Extended Hamilton Operators

In this paper, we introduce the class of extended Hamilton operators and study various properties of this class. We examine the decomposability of extended Hamilton operators. In addition,we prove that an extended Hamilton operator with property(δ) is subscalar. Finally, we consider Weyl type theorems of this class.     

Weyl numbers and eigenvalues of abstract summing operators

We estimate Weyl numbers and eigenvalues of operators via studying their abstract summing norms. In particular we prove estimates of these summing norms for abstract interpolation Lorentz spaces. For this we combine factorization theorems with estimates of concavity constants. Finally we apply our general eigenvalue results to integral operators with kernels of weakly singular type. We obtain asymptotically optimal estimates which extend the well-known classical results.     

On Locally Homogeneous G-structures

The notion of infinitesimal homogeneity is extended to arbitrary connections on G-structures. Two theorems of Singer type are proved for the extended notion. The results are applied to conformal and Weyl structures.     

广义特征值的Wilkinson条件数

1．引言H．Weyl于1912年证明了下述结果［1］．Weyl定理．设人B为nxn．Hermite矩阵，特征值分别为入λl≥λ2≥…≥λn和以1三v2三…三on，那么人一nilsilA—Bll。，；＝l，2，…，。，其中11112为矩阵的谱范数。这条定理已成为矩阵扰动理论中的标准结果，被推广到奇异值问题、广义特征值问题、广义奇异值问题［2］，所得结果可通称为W6yl型定理，在矩阵分析和矩阵计算中有广泛而重要的应用．我们注意到，就实际应用而言，使用稳定算法而得到的计算结果的精度分析问题，可以转化为小扰动情形下的扰动分析．此时。B是A的某个邻近矩阵，而…     

Singular conformable sequential differential equations with distributional potentials

In this paper we consider the singular conformable sequential equation with distributional potentials. We present Weyl’s theory in the frame of conformable derivatives. Moreover we give two theorems on limit-point case.     

Property (R) for Bounded Linear Operators

We introduce the spectral property (R), for bounded linear operators defined on a Banach space, which is related to Weyl type theorems. This property is also studied in the framework of polaroid, or left polaroid, operators.     

Row and Column Removal Theorems for Homomorphisms of Specht Modules and Weyl Modules

We prove a q-analogue of the row and column removal theorems for homomorphisms between Specht modules proved by Fayers and the first author [16]. These results can be considered as complements to James and Donkin’s row and column removal theorems for decomposition numbers of the symmetric and general linear groups. In this paper we consider homomorphisms between the Specht modules of the Hecke algebras of type A and between the Weyl modules of the q-Schur algebra.This research was supported by ARC grant DP0343023. The first author was also supported by a Sesqui Research Fellowship at the University of Sydney.     

Weyl transformations on manifolds I. Definitions and isomorphism theorems

In this paper we define Weyl's transformations on complete Riemannian manifolds and complete Weyl Quantization. We also prove two isomorphism theorems and give a useful trace formula and some other result. Supported by NNSFC     

On Duality Theorems for Nonsmooth Lipschitz Optimization Problems

A nonsmooth Lipschitz vector optimization problem (VP) is considered. Using the Fritz John type necessary optimality conditions for (VP), we formulate the Mond–Weir dual problem (VD) and establish duality theorems for (VP) and (VD) under (strict) pseudoinvexity assumptions on the functions. Our duality theorems do not require a constraint qualification.     

KKM type theorems and generalized vector equilibrium problems in noncompact FC-spaces

A new KKM type theorem is first proved under noncompact setting of FC-spaces. As applications of the KKM type theorem, we establish some new existence theorems of solutions for generalized vector equilibrium problems under noncompact setting of FC-spaces. These theorems improve and generalize many known results in literature.     

多目标变分问题的混合对偶性

本文给出了一类多目标变分问题的混合对偶 ,使得 Wolfe型对偶和 Mond-Weir型对偶是其特殊情况 ,并在函数 (F ,ρ) -凸性的条件下建立了多目标变分问题关于有效解的混合对偶理论 .     

Generalized KKM type theorems in FC-spaces with applications (II)

This paper is a continuum of the preceding paper of author. By applying a coincidence theorem in noncompact FC-space without any convexity structure due to author, a new KKM type theorem is first proved under noncompact setting of FC-spaces. The equivalent relation between the coincidence theorem and the KKM type theorem is also established. As applications of the KKM type theorem, we establish some new existence theorems of solutions for three classes of generalized vector equilibrium problems under noncompact setting of FC-spaces. These theorems improve and generalize many known results in literature.     

Inverse problems for Sturm–Liouville operators with interior discontinuities and boundary conditions dependent on the spectral parameter

In this paper, we discuss the inverse problem for Sturm–Liouville operators with arbitrary number of interior discontinuities and boundary conditions having fractional linear function of spectral parameter on the finite interval [0,1]. Using Weyl function techniques, we establish some uniqueness theorems for the Sturm–Liouville operator. Copyright © 2012 John Wiley & Sons, Ltd.     

Partial inverse nodal problems for differential pencils on a star-shaped graph

In this paper, the authors study partial inverse nodal problems for differential pencils on a star-shaped graph. We firstly show that the potential on each edge can be uniquely determined by twin-dense nodal subsets on some interior intervals under certain conditions. Without any nodal information on some potential on the fixed edge, we may add some spectral information to guarantee these uniqueness theorems. We still consider the case of arbitrary intervals having the internal vertex. In particular, we pose and solve a new partial inverse nodal problem for differential pencils on the star-shaped graph from the Weyl m-function and the theory concerning densities of zeros of entire functions.     

Weyl type theorems and hypercyclic operators II

In this note, the relation between hypercyclic operator matrices (or supercyclic operator matrices) and the operator matrices which satisfy Weyl type theorems is discussed. Also, using a variant of the essential approximate point spectrum, we give the necessary and sufficient conditions for for which a-Browder's theorem or a-Weyl's theorem holds.

     

Moudafi's viscosity approximations with Meir-Keeler contractions

In this paper, we discuss Moudafi's viscosity approximations with Meir-Keeler contractions. We first present very simple proofs of Xu's theorems concerning Moudafi's approximations. We next prove that Browder's and Halpern's type convergence theorems imply Moudafi's viscosity approximations. Using them, we finally state several deduced theorems.