有一致降指数的算子

本文讨论了有拓扑一致降指数的算子的可交换拟幂零摄动:举出反例说明有拓扑一致降指数的算子在可交换拟幂零摄动下是不稳定的;得到有拓扑一致降指数的算子和它的可交换拟幂零摄动的超值域与超核之间的关系;利用这些关系,证明了左(右)Drazin可逆算子在可交换幂零摄动下是稳定的.最后还讨论了Banach空间上B-正则类BR_i(1≤i≤13)中算子的R_i型Kato分解与R_i型超Kato分解.     

On the isolated points of the surjective spectrum of a bounded operator

For a bounded operator acting on a complex Banach space, we show that if is not surjective, then is an isolated point of the surjective spectrum of if and only if , where is the quasinilpotent part of and is the analytic core for . Moreover, we study the operators for which . We show that for each of these operators , there exists a finite set consisting of Riesz points for such that and is connected, and derive some consequences.

     

Distances between elements of a semigroup and estimates for derivatives

This paper is concerned first with the behaviour of differences T（t） - T（s） near the origin, where （T（t）） is a semigroup of operators on a Banach space, defined either on the positive real line or a sector in the right half-plane （in which case it is assumed analytic）. For the non-quasinilpotent case extensions of results in the published literature are provided, with best possible constants; in the case of quasinilpotent semigroups on the half-plane, it is shown that, in general, differences such as T（t） -T（2t） have norm approaching 2 near the origin. The techniques given enable one to derive estimates of other functions of the generator of the semigroup; in particular, conditions are given on the derivatives near the origin to guarantee that the semigroup generates a unital algebra and has bounded generator.     

Invariant subspaces for positive operators on locally convex solid Riesz spaces

We prove that an x₀-quasinilpotent semigroup S of continuous positive linear operators on a locally convex solid Riesz space X has a common invariant subspace. Using this, a result which implies the main theorem of Abramovich, Aliprantis and Burkinshaw [J. Funct. Anal. 115 (1993) 418424] is also given.     

Applications of the growth characteristics induced by the spectral distance

Let A be a complex unital Banach algebra. Using a connection between the spectral distance and the growth characteristics of a certain entire map into A, we derive a generalization of Gelfand’s famous power boundedness theorem. Elaborating on these ideas, with the help of a Phragm´en-Lindel¨of device for subharmonic functions, it is then shown, as the main result, that two normal elements of a C^?-algebra are equal if and only if they are quasinilpotent equivalent.     

The Iterated Aluthge Transform of an Operator

The Aluthge transform (defined below) of an operator T on Hilbert space has been studied extensively, most often in connection with p-hyponormal operators. In [6] the present authors initiated a study of various relations between an arbitrary operator T and its associated , and this study was continued in [7], in which relations between the spectral pictures of T and were obtained. This article is a continuation of [6] and [7]. Here we pursue the study of the sequence of Aluthge iterates { ⁽ⁿ⁾} associated with an arbitrary operator T. In particular, we verify that in certain cases the sequence { ⁽ⁿ⁾} converges to a normal operator, which partially answers Conjecture 1.11 in [6] and its modified version below (Conjecture 5.6). Submitted: December 5, 2000? Revised: August 30, 2001.     

拟幂零积分算子的等价刻划

本给出了一娄具有非负核函数的积分算子，并得到了该算子为拟零算子的充必要条件，该算子包括了重要的Hardy算子。     

Banach空间上的左可逆算子的稳定性

主要讨论了Banach空间上左可逆算子在线性运算上的稳定性及一些摄动问题，并通过反例证明了对于Banach空间上的左可逆算子A和B，R（A）∩R（B）＝{0}不是λA＋B（λ∈C）为左可逆算子的必要条件。