Group Inverses and Drazin Inverses over Banach Algebras
نویسنده
چکیده
For a matrix over a complex commutative unital Banach algebra, necessary and suucient conditions are given for the existence of its group inverse, and more generally, its Drazin inverses. The conditions are easy to check and explicit formulas for the inverses are provided. Some properties of the inverses and an application to operator theory are discussed. This note is a continuation of an earlier work of the author.
منابع مشابه
Generalized inverses in certain Banach algebras of operators∗
Let X be a Banach space and T be a bounded linear operator from X to itself (T ∈ B(X).) An operator S ∈ B(X) is a generalized inverse of T if TST = T . In this paper we look at several Banach algebras of operators and characterize when an operator in that algebra has a generalized inverse that is also in the algebra. Also, Drazin inverses will be related to generalized inverses and spectral pro...
متن کاملDrazin Inverses in Jörgens Algebras of Bounded Linear Operators
Let X be a Banach space and T be a bounded linear operator from X to itself (T ∈ B(X).) An operator D ∈ B(X) is a Drazin inverse of T if TD = DT , D = TD and T k = T D for some nonnegative integer k. In this paper we look at the Jörgens algebra, an algebra of operators on a dual system, and characterise when an operator in that algebra has a Drazin inverse that is also in the algebra. This resu...
متن کاملRepresentations for the Generalized Drazin Inverse in a Banach Algebra (communicated by Fuad Kittaneh)
The Drazin inverse has important applications in matrix theory and fields such as statistics, probability, linear systems theory, differential and difference equations, Markov chains, and control theory ([1, 2, 11]). In [9], Koliha extended the Drazin invertibility in the setting of Banach algebras with applications to bounded linear operators on a Banach space. In this paper, Koliha was able t...
متن کاملIterative methods for computing generalized inverses
In this article we extend the method of Yong-Lin Chen (Iterative methods for computing the generalized inverses A (2) T,S of a matrix A, Appl. Math. Comput. 75 (2-3) (1996)) to inifinite dimensional settings. Precisely, we construct an iterative method for computing outer generalized inverses of operators on Banach spaces, and also for computing the generalized Drazin inverse of Banach algebra ...
متن کاملDrazin Inverses of Operators with Rational Resolvent
Let A be a bounded linear operator on a Banach space such that the resolvent of A is rational. If 0 is in the spectrum of A, then it is well known that A is Drazin invertible. We investigate spectral properties of the Drazin inverse of A. For example we show that the Drazin inverse of A is a polynomial in A.
متن کامل