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Displaying similar documents to “Banach manifolds of algebraic elements in the algebra ℒ (H) of bounded linear operatorsof bounded linear operators”

Bounded symmetric domains and derived geometric structures

Wilhelm Kaup (2002)

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

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Every homogeneous circular convex domain D ⊂ C n (a bounded symmetric domain) gives rise to two interesting Lie groups: The semi-simple group G = A ⁢ u ⁢ t ⁢ D of all biholomorphic automorphisms of D and its isotropy subgroup K ⊂ G ⁢ L ⁢ n , C at the origin (a maximal compact subgroup of G ). The group G acts in a natural way on the compact dual X of D (a certain compactification of C n that generalizes the Riemann sphere in case D is the unit disk in C ). Various authors have studied the orbit structure of the G -space X , here...

Trace and determinant in Jordan-Banach algebras.

Bernard Aupetit, Abdelaziz Maouche (2002)

Publicacions Matemàtiques

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Using an appropriate definition of the multiplicity of a spectral value, we introduce a new definition of the trace and determinant of elements with finite spectrum in Jordan-Banach algebras. We first extend a result obtained by J. Zemánek in the associative case, on the connectedness of projections which are close to each other spectrally (Theorem 2.3). Secondly we show that the rank of the Riesz projection associated to a finite-rank element a and a finite subset of its spectrum is...

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 CR-structure of certain linear group orbits in infinite dimensions

Wilhelm Kaup (2004)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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For large classes of complex Banach spaces (mainly operator spaces) we consider orbits of finite rank elements under the group of linear isometries. These are (in general) real-analytic submanifolds of infinite dimension but of finite CR-codimension. We compute the polynomial convex hull of such orbits  M explicitly and show as main result that every continuous CR-function on  M has a unique extension to the polynomial convex hull which is holomorphic in a certain sense. This generalizes...

A glimpse at the theory of Jordan-Banach triple systems.

José M. Isidro (1989)

Revista Matemática de la Universidad Complutense de Madrid

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In this article, a survey of the theory of Jordan-Banach triple systems is presented. Most of the recent relevant results in this area have been included, though no proofs are given.

On isomorphisms of standard operator algebras

Lajos Molnár (2000)

Studia Mathematica

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We show that between standard operator algebras every bijective map with a certain multiplicativity property related to Jordan triple isomorphisms of associative rings is automatically additive.