Prediction Operators in Banach Ideal Spaces

A necessary and sufficient condition for an operator in a Banach ideal space to be a prediction operator is given.     

Eigenvalues of Set-Valued Operators in Banach Spaces

This work deals with the spectral analysis of set-valued operators from a Banach space X into its dual space X^*. The main goal of the paper is to study semicontinuity properties of the spectrum operator.Mathematics Subject Classifications (2000) 47H04, 47H12, 58C40.UMR 2071 Universidad de Chile-CNRS.     

Multipliers for p-Bessel Sequences in Banach Spaces

Multipliers have been recently introduced as operators for Bessel sequences and frames in Hilbert spaces. These operators are defined by a fixed multiplication pattern (the symbol) which is inserted between the analysis and synthesis operators. In this paper, we will generalize the concept of Bessel multipliers for p-Bessel and p-Riesz sequences in Banach spaces. It will be shown that bounded symbols lead to bounded operators. Symbols converging to zero induce compact operators. Furthermore, we will give sufficient conditions for multipliers to be nuclear operators. Finally, we will show the continuous dependency of the multipliers on their parameters.     

Optimal Weyl-type Inequalities for Operators in Banach Spaces

Let (s_n) be an s-number sequence. We show for each k = 1, 2, . . . and n ≥ k + 1 the inequality between the eigenvalues and s-numbers of a compact operator T in a Banach space. Furthermore, the constant (k + 1)^1/2 is optimal for n = k + 1 and k = 1, 2, . . .. This inequality seems to be an appropriate tool for estimating the first single eigenvalues. On the other hand we prove that the Weyl numbers form a minimal multiplicative s-number sequence and by a well-known inequality between eigenvalues and Weyl numbers due to A. Pietsch they are very good quantities for investigating the optimal asymptotic behavior of eigenvalues. Research of the second author was supported by the DFG Emmy-Noether grant Hi 584/2-3.     

Compact-Friendly Multiplication Operators on Banach Function Spaces

Answering a question posed by Abramovich et al. (Indag. Math.(N.S.)10 (1999), 161-171, we prove that a positive multiplication operator on an arbitrary Banach function space X is compact-friendly if and only if the multiplier is constant on a set of positive measure.     

On Diagonal Subdifferential Operators in Nonreflexive Banach Spaces

Consider a real-valued bifunction f defined on C ×C, where C is a closed and convex subset of a Banach space X, which is concave in its first argument and convex in its second one. We study its subdifferential with respect to the second argument, evaluated at pairs of the form (x,x), and the subdifferential of − f with respect to its first argument, evaluated at the same pairs. We prove that if f vanishes whenever both arguments coincide, these operators are maximal monotone, under rather undemanding continuity assumptions on f. We also establish similar results under related assumptions on f, e.g. monotonicity and convexity in the second argument. These results were known for the case in which the Banach space is reflexive and C = X. Here we use a different approach, based upon a recently established sufficient condition for maximal monotonicity of operators, in order to cover the nonreflexive and constrained case (C ≠ X). Our results have consequences in terms of the reformulation of equilibrium problems as variational inequality ones.     

复Banach空间上推广的Roper-Suffridge算子

从定义出发证明复Banach空间特定域上推广的Roper-Suffridge算子保持α次强β型螺形性及ρ次抛物型β型螺形性,由此得到推广后的算子在复Banach空间特定域上保持α次强星形性、ρ次抛物星形性及抛物星形性,为由复平面C中单位圆盘D上的α次强β型螺形映照及ρ次抛物β型螺形映照来构造复Banach空间特定域上相应的映照提供了一种新的途径,充实了对Roper-Suffridge算子的研究.     

Existence Theorems for Set-valued Operators in Banach Spaces

In this paper, we study the problem of existence of zero points for set-valued operators in Banach spaces. We present a simple condition which can be used to verify that under some conditions, set-valued operators have zero points. Furthermore, we derive the surjectivity result and the Kakutani fixed point theorem by using this condition.      

On Almost-Periodic Operators in the Spaces of Sequences

We study some properties of almost-periodic operators in the spaces l ^p and the spaces of Bohr and Besicovich almost-periodic sequences.     

一致平滑Banach空间中一类非线性算子的Ishikawa迭代序列的收敛定理

使用新的技巧，我们得到了连续强增生算子或连续强伪压缩算子的Ｉｓｈｉｋａｗａ迭代序列的强收敛定理，推广或改进了近期相关的结果．     

Banach 空间中多值非单调算子的相补问题

应用H-空间中的Park极大元定理,在Banach空间中证明了多值非单调算子的相补问题的解的存在性定理．     

Banach空间中的非线性增生算子随机方程

本文引进（ＪＭ）型算子的概念，并证明非线性增生算子和（ＪＭ）型算子随机方程的解的存在定理。     

Banach空间中线性算子的齐性广义逆

本文首先在Banach空间内引进拟线性投影算子的概念,由此给出Banach空 间内线性算子的齐性广义逆的统一定义。齐性广义逆包含线性广义逆、单值度量广义 逆.本文证得齐性广义逆存在的充分必要条件.     

Operators on Subspaces of Hereditarily Indecomposable Banach Spaces

We show that if X is a complex hereditarily indecomposable space,then every operator from a subspace Y of X to X is of the formI + S, where I is the inclusion map and S is strictly singular.1991 Mathematics Subject Classification 46B20, 47B99.     

Stampfli''''s Theorem for Operators on Some Banach Spaces

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On Positive Operators on Some Ordered Banach Spaces

In this paper we study to what extent some classical results concerning operators T, from a -space to a Banach space, or from a Banach space to a L ¹-space, can be precised, when the Banach spaces involved are ordered (by a normal cone in the first case, by a closed generating proper convex cone in the second case) and when the operators T are positive.     

K-Theory for Algebras of Operators on Banach Spaces

It is proved that, for each pair (m, n) of non-negative integers,there is a Banach space X for which K₀(B(X))Z^m and K₁(B(X))Zⁿ.The K-groups of all closed ideals of operators contained inthe ideal of strictly singular operators are computed, and someresults about the existence of splittings of certain short exactsequences are derived.     

巴拿赫空间中演化算子的非一致多项式膨胀性

给出了Banach空间中演化算子多项式膨胀性的三个概念,讨论了演化算子的非一致多项式膨胀性的积分特征.且作为应用,利用Lyapunov函数给出了相应概念的刻画.从而将演化型算子指数膨胀性理论的相关经典结论推广到了多项式膨胀的情形.