LINEAR OPERATORS WITH EMPTY SPECTRUM

IF 0.6 4区 数学 Q3 MATHEMATICS
Morisuke HASUMI, Michio SETO
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引用次数: 0

Abstract

In this note we are interested in showing a simple property which characterizes linear operators having empty spectrum on complex Banach spaces. Although it is rather well known that such operators exist, the current literature deals with very few such examples,only as an exercise topic. Our characterization says that such operators are in one-to-one correspondence with injective quasinilpotent operators. This means that the purely unbounded property of linear operators can be reduced to the bounded one. In fact, we obtain a simple way to test and construct examples of such operators and then proceed to make observations of some interest from the function-theoretic point of view. For instance, we define an analogue of the order in the theory of entire functions and show the existence of operators of all order types.
具有空谱的线性算子
在这篇笔记中,我们感兴趣的是给出复巴拿赫空间上具有空谱的线性算子的一个简单性质。虽然这类运算符的存在是众所周知的,但目前的文献很少涉及这类例子,只是作为一个练习主题。我们的刻画表明这样的算子与内射拟幂算子是一一对应的。这意味着线性算子的纯无界性质可以简化为有界性质。事实上,我们获得了一种简单的方法来测试和构造这些算子的例子,然后从函数论的角度进行一些有趣的观察。例如,我们在全函数理论中定义了阶的类比,并证明了所有阶类型算子的存在性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
0.80
自引率
0.00%
发文量
10
审稿时长
>12 weeks
期刊介绍: The Kyushu Journal of Mathematics is an academic journal in mathematics, published by the Faculty of Mathematics at Kyushu University since 1941. It publishes selected research papers in pure and applied mathematics. One volume, published each year, consists of two issues, approximately 20 articles and 400 pages in total. More than 500 copies of the journal are distributed through exchange contracts between mathematical journals, and available at many universities, institutes and libraries around the world. The on-line version of the journal is published at "Jstage" (an aggregator for e-journals), where all the articles published by the journal since 1995 are accessible freely through the Internet.
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