Displaying similar documents to “Isometries and automorphisms of the spaces of spinors.”

The set of automorphisms of B(H) is topologically reflexive in B(B(H))

Lajos Molnár (1997)

Studia Mathematica

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The aim of this paper is to prove the statement announced in the title which can be reformulated in the following way. Let H be a separable infinite-dimensional Hilbert space and let Φ: B(H) → B(H) be a continuous linear mapping with the property that for every A ∈ B(H) there exists a sequence ( Φ n ) of automorphisms of B(H) (depending on A) such that Φ ( A ) = l i m n Φ n ( A ) . Then Φ is an automorphism. Moreover, a similar statement holds for the set of all surjective isometries of B(H).

On the automorphisms of the spectral unit ball

Jérémie Rostand (2003)

Studia Mathematica

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Let Ω be the spectral unit ball of Mₙ(ℂ), that is, the set of n × n matrices with spectral radius less than 1. We are interested in classifying the automorphisms of Ω. We know that it is enough to consider the normalized automorphisms of Ω, that is, the automorphisms F satisfying F(0) = 0 and F'(0) = I, where I is the identity map on Mₙ(ℂ). The known normalized automorphisms are conjugations. Is every normalized automorphism a conjugation? We show that locally, in a neighborhood of a...

Notes on automorphisms of ultrapowers of II₁ factors

David Sherman (2009)

Studia Mathematica

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In functional analysis, approximative properties of an object become precise in its ultrapower. We discuss this idea and its consequences for automorphisms of II₁ factors. Here are some sample results: (1) an automorphism is approximately inner if and only if its ultrapower is ℵ₀-locally inner; (2) the ultrapower of an outer automorphism is always outer; (3) for unital *-homomorphisms from a separable nuclear C*-algebra into an ultrapower of a II₁ factor, equality of the induced traces...

Jordan automorphisms of triangular algebras. II

Driss Aiat Hadj Ahmed, Rachid Tribak (2015)

Commentationes Mathematicae Universitatis Carolinae

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We give a sufficient condition under which any Jordan automorphism of a triangular algebra is either an automorphism or an anti-automorphism.

Holomorphic automorphism groups in certain compact operator spaces

Carlo Petronio (1990)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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A class of Banach spaces of compact operators in Hilbert spaces is introduced, and the holomorphic automorphism groups of the unit balls of these spaces are investigated.

Holomorphic automorphisms and collective compactness in J*-algebras of operator

José Isidro (2007)

Open Mathematics

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Let G be the Banach-Lie group of all holomorphic automorphisms of the open unit ball B 𝔄 in a J*-algebra 𝔄 of operators. Let 𝔉 be the family of all collectively compact subsets W contained in B 𝔄 . We show that the subgroup F ⊂ G of all those g ∈ G that preserve the family 𝔉 is a closed Lie subgroup of G and characterize its Banach-Lie algebra. We make a detailed study of F when 𝔄 is a Cartan factor.

2-local Jordan automorphisms on operator algebras

Ajda Fošner (2012)

Studia Mathematica

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We investigate 2-local Jordan automorphisms on operator algebras. In particular, we show that every 2-local Jordan automorphism of the algebra of all n× n real or complex matrices is either an automorphism or an anti-automorphism. The same is true for 2-local Jordan automorphisms of any subalgebra of ℬ which contains the ideal of all compact operators on X, where X is a real or complex separable Banach spaces and ℬ is the algebra of all bounded linear operators on X.