On generalized semi B-Fredholm operators

Unbounded generalized B-Fredholm operators

“…Here, in this paper, we will consider unbounded generalized B-Fredholm operators defined on a Banach space. Our work, in this paper, extend some results obtained in [12] to the case of unbounded operators. After an introductory section, we recall in section 2 a list of well known definitions which are must be required, in this paper.…”

“…Remark 2.2. Note that Definition 2.4 is equivalent to the definitions given in the case of bounded operators in [10,12]. In the case of Hilbert space, it is equivalent to the definition given in [6].…”

“…It is well known that, the class of B-Fredholm operators was first introduced by M. Berkani in [2] in the bounded case in Banach space, and it was generalized by Berkani and Castro-González in [4] to unbounded operators in Hilbert space. Newly, this notion of operators was extended by García et al in [12] to generalized B-Fredholm operators, in the case of bounded linear operators defined on a Banach space. In this section, we shall study this theory in the case of unbounded operators defined from X to X.…”

“…This notion of operators was generalized by Berkani and Castro-González in [4] to unbounded operators in Hilbert space. Recently, this class of operators was extended and studied by O. García et al in [12] to generalized bounded B-Fredholm operators acting on a Banach space. Here, in this paper, we will consider unbounded generalized B-Fredholm operators defined on a Banach space.…”