Glasnik matematički, Vol. 46 No. 2, 2011.
Original scientific paper
https://doi.org/10.3336/gm.46.2.12
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
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.
Keywords
Products of operators; bounded and unbounded operators; self-adjoint; closed and normal operators
Hrčak ID:
74270
URI
Publication date:
23.11.2011.
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