Banach代数中两个元素之和广义Drazin逆的表示

Representations for Generalized Drazin Inverses of Sum of Two Elements in Banach Algebra

利用Banach代数中的幂等系统考虑两个元素之和的广义Drazin逆,给出了Banach代数中的两个元素a,b,在b^2a=a~πbabb~π,a^2b=a~πabab~π的条件下其和a+b的广义Drazin逆的表达式.

Using the system of idempotents in a Banach algebra,we considered the generalized Drazin inverse of the sum of two elements.For two elements a,b in a Banach algebra,we gave the expressions for the generalized Drazin inverse of the suma＋b under the condition that b^2a=a~πbabb~π,a^2b=a~πabab~π.