良性有界算子理论综述

良性有界算子在数学的许多领域都有十分重要的应用,如应用于斯图姆-刘维尔理论,富里叶分析与乘数理论2,3].尽管良性有界算子理论已经建立,但仍有许多未解决的有意义的问题.近几年,出现不少有意义的工作,包括含共轭理论的完备良性有界算子理论,紧良性有界算子理论的建立等.本综述将着重于这些方面并概述一些新进展,同时提出一些仍未解决的问题.

A SURVEY OF THE THEORY OF WELL- BOUNDED OPERATORS

The theory of well bounded operators has been found many applications and formed deep connections with other areas of mathematics.For example,it has been applied successfully to Sturm Liouville theory,Fourier analysis and multiplier theory .Although the theory of well bounded operators is well established,there are a number of unresolved and interesting questions which are potentially fruitful areas for further research.In recent yeas,many significant works have been done toward to answer some of these questions,to correct and clarify certain aspects of the theory,and to establish a more complete well bounded operator theory including a dual theory on general Banach spaces and a theory of compact well bounded operators.In this survey we shall focus on those aspects and summarize some new progress.We also arise several problems which are still open.