Nonlinear preservers involving quadratic operators

Autor:	M. Oudghiri, K. Souilah
Rok vydání:	2021
Předmět:	Surjective function symbols.namesake Pure mathematics Nonlinear system Quadratic equation General Mathematics Bounded function Linear operators Hilbert space symbols Complex number Mathematics Bounded operator
Zdroj:	Analysis Mathematica. 47:867-879
ISSN:	1588-273X 0133-3852
DOI:	10.1007/s10476-021-0103-9
Popis:	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 $${\cal B}(H)$$ 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 $$S,T \in {\cal B}(H)$$ and λ ∈ ℂ.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::61df65b09c0dd1268cd986a80fc54214 https://doi.org/10.1007/s10476-021-0103-9 Zobrazit plný text záznamu Full text from SpringerLink