Cline’s formula and Jacobson’s lemma for g-Drazin inverse
نویسندگان
چکیده
We present new conditions under which Cline?s formula and Jacobson?s lemma for g-Drazin inverse hold. Let A be a Banach algebra, let a,b ? satisfying akbkak = ak+1 some k N. prove that has if only bkak inverse. In this case, (bkak)d bk(ad)2ak ad ak[(bkak)d]k+1. Further, we study in algebra the preceding condition. The common spectral property of bounded linear operators on space is thereby obtained.
منابع مشابه
Cline’s formula for the generalized Drazin inverse
†Department of Mathematics, Southeast University, Nanjing 210096, China ‡College of Mathematics and Information Science, Guangxi University, Nanning 530004, China E-mail: [email protected] E-mail: [email protected] E-mail: [email protected] Abstract: It is well known that for an associative ring R, if ab is Drazin invertible then ba is Drazin invertible. In this case, (ba)D = b((ab)D)2a. This for...
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ژورنال
عنوان ژورنال: Filomat
سال: 2021
ISSN: ['2406-0933', '0354-5180']
DOI: https://doi.org/10.2298/fil2115083c