关于B-凸空间及其上黎斯算子West分解

给出 Ｂａｎａｃｈ空间列｛Ｘｉ｝ｉ＝１∞的 ｌｐ乘积Ｂ－凸的特征刻划, 证明Ｂ－凸空间上的每个黎斯算子可Ｗｅｓｔ分解,即分解成一个紧算子和一个拟幂 零算子的和．     

Quotients of partial abelian monoids and the Riesz decomposition property

Partial abelian monoids (PAMs) are structures (), where is a partially defined binary operation with domain , which is commutative and associative in a restricted sense, and 0 is the neutral element. PAMs with the Riesz decomposition properties and binary relations with special properties on PAMs are studied. Relations with abelian groups, dimension equivalence and K ₀ for AF C^*-algebras are discussed. Received September 17, 2000; accepted in final form March 13, 2002.     

Invariant sublattices for positive operators

There are, by now, many results which guarantee that positive operators on Banach lattices have non-trivial closed invariant sublattices. In particular, this is true for every positive compact operator. Apart from some results of a general nature, in this paper we present several examples of positive operators on Banach lattices which do not have non-trivial closed invariant sublattices. These examples include both AM-spaces and Banach lattices with an order continuous norm and which are and are not atomic. In all these cases we can ensure that the operators do possess non-trivial closed invariant subspaces.     

Vector lattices of weakly compact operators on Banach lattices

A result of Aliprantis and Burkinshaw shows that weakly compact operators from an AL-space into a KB-space have a weakly compact modulus. Groenewegen characterised the largest class of range spaces for which this remains true whenever the domain is an AL-space and Schmidt proved a dual result. Both of these authors used vector-valued integration in their proofs. We give elementary proofs of both results and also characterise the largest class of domains for which the conclusion remains true whenever the range space is a KB-space. We conclude by studying the order structure of spaces of weakly compact operators between Banach lattices to prove results analogous to earlier results of one of the authors for spaces of compact operators.

     

广义框架和广义Riesz基的摄动

引入并研究了Banach空间X中的Bessel集、广义框架与广义Riesz基．对X中的任一Bessel集{gm}m∈M，定义有界线性算子T：L^2（P）→X^＊，利用算子丁，给出了Bessel集与广义框架的等价刻画．同时讨论了广义框架和广义Riesz基的摄动．     

锥中上调和函数的Riesz 分解定理及其应用

本文给出了锥中上调和函数的Riesz 分解定理. 同时, 得到了它在锥中无穷远点处的增长性质, 并且刻画了其例外集的几何性质. 作为应用, 我们证明了锥内次调和函数的Phragmén-Lindelöf 型定理.     

On positive unipotent operators on Banach lattices

Let be a positive operator on a complex Banach lattice. We prove that is greater than or equal to the identity operator if

     

Limiting weak-type behaviors for Riesz transforms and maximal operators in Bessel setting

We establish the limiting weak type behaviors of Riesz transforms associated to the Bessel operators on IR+. which are closely related to the best constants of the weak type (1,1) estimates for such operators. Meanwhile, the corresponding results for Hardy-Littlewood maximal operator and fractional maximal operator in Bessel setting are also obtained.     

The finite-dimensional decomposition property in non-Archimedean Banach spaces

A non-Archimedean Banach space has the orthogonal finite-dimensional decomposition property（OFDDP） if it is the orthogonal direct sum of a sequence of finite-dimensional subspaces.This property has an influence in the non-Archimedean Grothendieck＇s approximation theory,where an open problem is the following： Let E be a non-Archimedean Banach space of countable type with the OFDDP and let D be a closed subspace of E.Does D have the OFDDP？ In this paper we give a negative answer to this question; we construct a Banach space of countable type with the OFDDP having a one-codimensional subspace without the OFDDP.Next we prove that,however,for certain classes of Banach spaces of countable type,the OFDDP is preserved by taking finite-codimensional subspaces.     

Bands in lattices of operators

We consider the lattice of regular operators on a Dedekind complete Banach lattice. We show that in general the projection onto a band generated by a lattice homomorphism need not be continuous and that the principal bands need not be closed for the operator norm. In fact it is possible to find a convergent sequence of operators all the members of which are disjoint from the limit.

     

Characterizations of some classes of relatively regular operators

A bounded linear operator A on a Banach space is called relatively regular, if there is a bounded linear operator B such that ABA=A. In this case B is called a g₁-inverse of A. In this paper we characterize some classes of relatively regular operators A via the set {B₁-B₂:B₁ and B₂ are g₁-inverses of A}.     

A note on Riesz spaces with property-b

We study an order boundedness property in Riesz spaces and investigate Riesz spaces and Banach lattices enjoying this property.     

Slice regular composition operators

In the article, we study the theory of slice regular compositions. Especially, the Littlewood subordination principle and the Denjoy–Wolff-type theorem are established for slice regular functions.     

Almansi decomposition for Dunkl operators

Let Ωbe a G-invariant convex domain in RN including 0, where G is a Coxeter group associated with reduced root system R. We consider functions f defined in Ωwhich are Dunkl polyharmonic, i.e. (△h)nf =0 for some integer n. Here △h=∑j=1N Dj2 is the Dunkl Laplacian, and Dj is the Dunkl operator attached to the Coxeter group G, where kv is a multiplicity function on R and σv is the reflection with respect to the root v. We prove that any Dunkl polyharmonic function f has a decomposition of the form f(x)=f0(x) |x|2f1(x) … |x|2(n-1)fn-1(x),(?)x∈Ω, where fj are Dunkl harmonic functions, i.e. △hfj = 0. This generalizes the classical Almansi theorem for polyharmonic functions as well as the Fischer decomposition.     

The multisublinear maximal type operators in Banach function lattices

The main aim of this paper is to study a general multisublinear operators generated by quasi-concave functions between weighted Banach function lattices. These operators, in particular, generalize the Hardy–Littlewood and fractional maximal functions playing an important role in harmonic analysis. We prove that under some general geometrical assumptions on Banach function lattices two-weight weak type and also strong type estimates for these operators are true. To derive the main results of this paper we characterize the strong type estimate for a variant of multilinear averaging operators. As special cases we provide boundedness results for fractional maximal operators in concrete function spaces.     

On Some Expressions for the Riesz Angles of Orlicz Sequence Spaces

We obtain some expressions for the Riesz angles of Orlicz sequence spaces endowed with the Luxemburg and Orlicz norms and show some practical ways of computation.     

Polynomially Riesz perturbations

In this paper we investigate perturbation of left (right) Fredholm, Weyl and Browder operators by polynomially Riesz operators. We show how Baklouti’s idea of “communication” enhances the perturbation properties of polynomially Riesz operators.