Journal of University of Chinese Academy of Sciences >
Additive maps preserving the nullity or deficiency of operators
Received date: 2013-06-21
Revised date: 2013-09-09
Online published: 2014-09-15
Let B(X) and B(Y) be the Banach algebras of all bounded linear operators on infinite dimensional complex Banach spaces X and Y, respectively. It is proved that an additive surjective map φ from B(X) to B(Y) preserves the nullity in both directions if and only if there exists invertible bounded linear or conjugate linear operators U:X→Y and V:Y→X, such that φ(T)=UTV for all T∈B(X). A form for additive surjective maps preserving the deficiency in both directions is also obtained.
Key words： nullity; deficiency; additive maps
LI Chenxin , JI Guoxing . Additive maps preserving the nullity or deficiency of operators[J]. Journal of University of Chinese Academy of Sciences, 2014 , 31(5) : 590 -594 . DOI: 10.7523/j.issn.2095-6134.2014.05.003
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