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 کاملReverse order laws for {1, 3, 4}-generalized inverses in C*-algebras
In this paper, we consider the reverse order laws for {1, 3, 4}-generalized inverses in C*algebras. We present purely algebraic necessary and sufficient conditions for b{1, 3, 4}· a{1, 3, 4} ⊆ (ab){1, 3, 4} and (ab){1, 3, 4} = b{1, 3, 4} · a{1, 3, 4}. Also, we prove that (ab){1, 3, 4} ⊆ b{1, 3, 4} · a{1, 3, 4} is actually equivalent to (ab){1, 3, 4} = b{1, 3, 4} · a{1, 3, 4}. 2010 Mathematics S...
متن کاملGroup Inverses and Drazin Inverses over Banach Algebras
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 earl...
متن کاملGeneralized Inverses and Applications
Fredholm’s method to solve a particular integral equation in 1903, was probably the first written work on generalized inverses. In 1906, Moore formulated the generalized inverse of a matrix in an algebraic setting, which was published in 1920, and in the thirties von Neumann used generalized inverses in his studies of continuous geometries and regular rings. Kaplansky and Penrose, in 1955, inde...
متن کاملCharacterizations of Generalized Uniserial Algebras. Ii
Let SI be a finite dimensional algebra with unit element over a field. 21 is generalized uniserial if every primitive (left or right) ideal has a unique composition series. 21 is a UMFR algebra (an algebra with a unique minimal faithful representation) if 21 has only one faithful representation which is minimal with respect to being faithful. The notation used in this paper will be that of an e...
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ژورنال
عنوان ژورنال: Studia Mathematica
سال: 1993
ISSN: 0039-3223,1730-6337
DOI: 10.4064/sm-106-2-129-138