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1
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Exponentials of normal operators and commutativity of operators: a new approach

100%
Mortad M.
Colloquium Mathematicum
|
2011
|
tom 125
|
nr 1
1-6
EN
We present a new approach to the question of when the commutativity of operator exponentials implies that of the operators. This is proved in the setting of bounded normal operators on a complex Hilbert space. The proofs are based on some results on similarities by Berberian and Embry as well as the celebrated Fuglede theorem.
2
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Exponentials of bounded normal operators

63%
Chaban A., Mortad M.
Colloquium Mathematicum
|
2013
|
tom 133
|
nr 2
237-244
EN
The present paper is mainly concerned with equations involving exponentials of bounded normal operators. Conditions implying commutativity of normal operators are given, without using the known 2πi-congruence-free hypothesis. This is a continuation of a recent work by the second author.
3
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Generalizations of Kaplansky's Theorem Involving Unbounded Linear Operators

63%
Benali A., Mortad M.
Bulletin of the Polish Academy of Sciences. Mathematics
|
2014
|
tom 62
|
nr 2
181-186
EN
We are mainly concerned with the result of Kaplansky on the composition of two normal operators in the case in which at least one of the operators is unbounded.
4
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A topological characterization of the product of two closed operators

51%
Messirdi B., Mortad M., Azzouz A., Djellouli G.
Colloquium Mathematicum
|
2008
|
tom 112
|
nr 2
269-278
EN
The purpose of this work is to give a topological condition for the usual product of two closed operators acting in a Hilbert space to be closed.
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