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We present new additive results for the group inverse in a Banach algebra under certain perturbations. The upper bound of $|(a+b)^{#}-a^d|$ is thereby given. These extend the main results in [X. Liu, Y. Qin and H. Wei, Perturbation bound of the group inverse and the generalized Schur complement in Banach algebra, Abstr. Appl. Anal., 2012, 22 pages. DOI:10.1155/2012/629178].
In this paper, we introduce a weak group inverse (called the WG inverse in the present paper) for square matrices of an arbitrary index, and give some of its characterizations and properties. Furthermore, we introduce two orders: one is a pre-order a
In this article the $(b, c)$-inverse will be studied. Several equivalent conditions for the existence of the $(b,c)$-inverse in rings will be given. In particular, the conditions ensuring the existence of the $(b,c)$-inverse, of the annihilator $(b,c
An arbitrary group action on an algebra $R$ results in an ideal $mathfrak{r}$ of $R$. This ideal $mathfrak{r}$ fits into the classical radical theory, and will be called the radical of the group action. If $R$ is a noetherian algebra with finite GK-d
A strong inspiration for studying perturbation theory for fractional evolution equations comes from the fact that they have proven to be useful tools in modeling many physical processes. In this paper, we study fractional evolution equations of order
In this paper, we introduce a new technique in the study of the $*$-regular closure of some specific group algebras $KG$ inside $mathcal{U}(G)$, the $*$-algebra of unbounded operators affiliated to the group von Neumann algebra $mathcal{N}(G)$. The m