Linear Preservers of Quadratic Operators

Let B ( H ) be the algebra of all bounded linear operators on an infinite-dimensional complex Hilbert space H . In this paper, we get a complete classification of surjective linear maps on B ( H ) that preserve quadratic operators in both directions. An analogue result in the setting of finite-dimen...

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Bibliographic Details
Published in:Mediterranean journal of mathematics 2016-12, Vol.13 (6), p.4929-4938
Main Authors: Oudghiri, Mourad, Souilah, Khalid
Format: Article
Language:English
Subjects:
Hilbert space
Linear operators
Mathematics
Mathematics and Statistics
Operators (mathematics)
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Summary:Let B ( H ) be the algebra of all bounded linear operators on an infinite-dimensional complex Hilbert space H . In this paper, we get a complete classification of surjective linear maps on B ( H ) that preserve quadratic operators in both directions. An analogue result in the setting of finite-dimensional Banach spaces is given.
ISSN:1660-5446
1660-5454
DOI:10.1007/s00009-016-0783-8