Glasnik Matematicki, Vol. 46, No. 2 (2011), 433438.
AN IMPLICIT DIVISION OF BOUNDED AND
UNBOUNDED LINEAR OPERATORS WHICH PRESERVES THEIR PROPERTIES
Mohammed Hichem Mortad
Département de Mathématiques,
Université d'Oran (Essenia),
B.P. 1524, El Menouar, Oran 31000,
Algeria
email: mhmortad@gmail.com & mortad@univoran.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,
selfadjoint, closed and normal operators.
Full text (PDF) (access from subscribing institutions only)
DOI: 10.3336/gm.46.2.12
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