Representations for the pseudo Drazin inverse of elements in a Banach algebra
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...
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| Outros Autores: | , |
| Formato: | article |
| Idioma: | eng |
| Publicado em: |
2015
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| Assuntos: | |
| Texto completo: | http://hdl.handle.net/1822/32355 |
| País: | Portugal |
| Oai: | oai:repositorium.sdum.uminho.pt:1822/32355 |
| 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. |
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