Glasnik Matematicki, Vol. 46, No. 2 (2011), 433-438.

AN IMPLICIT DIVISION OF BOUNDED AND UNBOUNDED LINEAR OPERATORS WHICH PRESERVES THEIR PROPERTIES

Mohammed Hichem Mortad

Département de Mathématiques, Université d'Oran (Es-senia), B.P. 1524, El Menouar, Oran 31000, Algeria
e-mail: mhmortad@gmail.com & mortad@univ-oran.dz


Abstract.   We give an answer to the following problem: Given two linear operators A and B such that BA and A verify some property P, then when does B verify the same property P? Of course, we have to assume that B satisfies some condition Q independent of (or weaker than) P. This problem is solved in the setting of both bounded and unbounded operators on a Hilbert space. Some interesting counterexamples are also given.

2000 Mathematics Subject Classification.   47A05.

Key words and phrases.   Products of operators, bounded and unbounded operators, self-adjoint, closed and normal operators.


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DOI: 10.3336/gm.46.2.12


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