Multiplicative maps that are close to an automorphism on algebras of linear transformations

• Autorzy: L. W. Marcoux , H. Radjavi , A. R. Sourour
• Języki publikacji: EN

Abstrakty

EN

Let 𝓗 be a complex, separable Hilbert space of finite or infinite dimension, and let ℬ(𝓗) be the algebra of all bounded operators on 𝓗. It is shown that if φ: ℬ(𝓗) → ℬ(𝓗) is a multiplicative map(not assumed linear) and if φ is sufficiently close to a linear automorphism of ℬ(𝓗) in some uniform sense, then it is actually an automorphism; as such, there is an invertible operator S in ℬ(𝓗) such that $φ(A) = S^{-1} AS$ for all A in ℬ(𝓗). When 𝓗 is finite-dimensional, similar results are obtained with the mere assumption that there exists a linear functional f on ℬ(𝓗) so that f ∘ φ is close to f ∘ μ for some automorphism μ of ℬ(𝓗).

Kategorie tematyczne

• 47A30: Norms (inequalities, more than one norm, etc.)
• 47B49: Transformers, preservers (operators on spaces of operators)
• 15A24: Matrix equations and identities
• 15A04: Linear transformations, semilinear transformations
• 15A30: Algebraic systems of matrices

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2013
• Tom: 214
• Numer: 3
• Strony: 279-296

Daty

wydano

2013

Twórcy

autor

L. W. Marcoux

• Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1

autor

H. Radjavi

• Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1

autor

A. R. Sourour

• Department of Mathematics and Statistics, University of Victoria, Victoria, BC, Canada V8W 3P4

Identyfikatory

DOI

10.4064/sm214-3-6