Invertibility And Fredholm Properties For Linear Combinations Of Operators

Firstly,the research backgroound of linear combinations of operators with closed range is briefly outlined.Then,we mainly research the in-vertibility and Fredholmness for linear combinations of two operators with closed range.By means of space dcomposition and the skill of block oper-ator matrix,we transform ?A +?B into upper triangular operator matrix,where ?,??C\{0}.By using the properties of upper triangular opera-tor matrix,it is given that the sufficient and necessary conditions for the invertibility and Fredholmness for linear combinations of bounded linear operators with closed range,respectively,and then some related results about linear combinations of special operators are obtained.In addition,we give example to illustrate effectiveness of our results.