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• # Artykuł - szczegóły

## Studia Mathematica

2013 | 214 | 3 | 279-296

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

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).

279-296

wydano
2013

### Twórcy

autor
• Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
autor
• Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
autor
• Department of Mathematics and Statistics, University of Victoria, Victoria, BC, Canada V8W 3P4