A Note on Drazin Invertibility for Upper Triangular Block Operators

作者：Zguitti Hassane^*

来源：Mediterranean Journal of Mathematics, 2013, 10(3): 1497-1507.

DOI：10.1007/s00009-013-0275-z

• Upper triangular block operator
• Drazin spectrum
• single-valued extension property

A bounded linear operator A acting on a Banach space X is said to be an upper triangular block operators of order n, and we write A is an element of UTn(X), if there exists a decomposition of X = X-1 circle plus ... circle plus X-n and an n x n matrix operator (A(i,j))(1 <= i,j <= n) such that A = (A(i,j))(1 <= i,j <= n), A(i,j) = 0 for i > j. In this note we characterize a large set of entries A(i,j) with j > i such that sigma(D)(A) = n boolean OR(n)(i=1)sigma D(A(i,i));where sigma(D)(.) is the Drazin spectrum. Some applications concerning the Fredholm theory and meromorphic operators are given.

• 出版日期2013-8