Nonlinear preservers involving quadratic operators

Given two different complex numbers a and b , a bounded linear operator T acting on an infinite-dimensional complex Hilbert space H is said to be { a, b }-quadratic if ( T − a )( T − b ) = 0. We provide in this paper a complete description of all surjective maps Φ (not necessarily additive) on the a...

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Bibliographic Details
Published in:Analysis mathematica (Budapest) 2021-12, Vol.47 (4), p.867-879
Main Authors: Oudghiri, M., Souilah, K.
Format: Article
Language:English
Subjects:
Analysis
Complex numbers
Hilbert space
Linear operators
Mathematics
Mathematics and Statistics
Operators (mathematics)
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Summary:Given two different complex numbers a and b , a bounded linear operator T acting on an infinite-dimensional complex Hilbert space H is said to be { a, b }-quadratic if ( T − a )( T − b ) = 0. We provide in this paper a complete description of all surjective maps Φ (not necessarily additive) on the algebra ℬ ( H ) of all bounded linear operators on H that satisfy S − λT is { a, b }-quadratic if and only if Φ( S ) − λΦ ( T ) is { a, b }-quadratic for every S , T ∈ ℬ ( H ) and λ ∈ ℂ.
ISSN:0133-3852
1588-273X
DOI:10.1007/s10476-021-0103-9