Publicação
Representations for the pseudo Drazin inverse of elements in a Banach algebra
| Resumo: | In this paper, we investigate the pseudo Drazin invertibility of the sum and the product of elements in a Banach algebra {A}. Given pseudo Drazin invertible elements a and b such that a2b=aba and b2a=bab, it is shown that ab is pseudo Drazin invertible and a+b is pseudo Drazin invertible if and only if so is 1+a^\ddag b, and the related formulae are provided. |
|---|---|
| Autores principais: | Zhu, Huihui |
| Outros Autores: | Chen, Jianlong; Patrício, Pedro |
| Assunto: | Pseudo Drazin inverse Strongly spectral idempotent Jacobson radical Ciências Naturais::Matemáticas |
| Ano: | 2015 |
| País: | Portugal |
| Tipo de documento: | artigo |
| Tipo de acesso: | acesso restrito |
| Instituição associada: | Universidade do Minho |
| Idioma: | inglês |
| Origem: | RepositóriUM - Universidade do Minho |
| Resumo: | In this paper, we investigate the pseudo Drazin invertibility of the sum and the product of elements in a Banach algebra {A}. Given pseudo Drazin invertible elements a and b such that a2b=aba and b2a=bab, it is shown that ab is pseudo Drazin invertible and a+b is pseudo Drazin invertible if and only if so is 1+a^\ddag b, and the related formulae are provided. |
|---|