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Czasopisma help

  1. 3 Studia Mathematica

Autorzy help

  1. 3 Berkani M.

  2. 1 Sarih M.

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  1. 1 2001

  2. 1 2000

  3. 1 1996

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1
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Restriction of an operator to the range of its powers

100%
Berkani M.
Studia Mathematica
|
2000
|
tom 140
|
nr 2
163-175
EN
Let T be a bounded linear operator acting on a Banach space X. For each integer n, define $T_n$ to be the restriction of T to $ R(T^n) $ viewed as a map from $R(T^n)$ into $R(T^n)$. In [1] and [2] we have characterized operators T such that for a given integer n, the operator $T_n$ is a Fredholm or a semi-Fredholm operator. We continue those investigations and we study the cases where $T_n$ belongs to a given regularity in the sense defined by Kordula and Müller in[10]. We also consider the regularity of operators with topological uniform descent.
2
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Idempotents dans les algèbres de Banach

100%
Berkani M.
Studia Mathematica
|
1996
|
tom 120
|
nr 2
155-158
EN
Using the holomorphic functional calculus we give a characterization of idempotent elements commuting with a given element in a Banach algebra.
3
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An Atkinson-type theorem for B-Fredholm operators

63%
Berkani M., Sarih M.
Studia Mathematica
|
2001
|
tom 148
|
nr 3
251-257
EN
Let X be a Banach space and let T be a bounded linear operator acting on X. Atkinson's well known theorem says that T is a Fredholm operator if and only if its projection in the algebra L(X)/F₀(X) is invertible, where F₀(X) is the ideal of finite rank operators in the algebra L(X) of bounded linear operators acting on X. In the main result of this paper we establish an Atkinson-type theorem for B-Fredholm operators. More precisely we prove that T is a B-Fredholm operator if and only if its projection in the algebra L(X)/F₀(X) is Drazin invertible. We also show that the set of Drazin invertible elements in an algebra A with a unit is a regularity in the sense defined by Kordula and Müller [8].
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