Banach manifolds of algebraic elements in the algebra $$\mathcal{L}$$ (H) of bounded linear operatorsof bounded linear operators

• Autorzy: José Isidro
• Języki publikacji: EN

Abstrakty

EN

Given a complex Hilbert space H, we study the manifold $$\mathcal{A}$$ of algebraic elements in $$Z = \mathcal{L}\left( H \right)$$ . We represent $$\mathcal{A}$$ as a disjoint union of closed connected subsets M of Z each of which is an orbit under the action of G, the group of all C*-algebra automorphisms of Z. Those orbits M consisting of hermitian algebraic elements with a fixed finite rank r, (0< r<∞) are real-analytic direct submanifolds of Z. Using the C*-algebra structure of Z, a Banach-manifold structure and a G-invariant torsionfree affine connection ∇ are defined on M, and the geodesics are computed. If M is the orbit of a finite rank projection, then a G-invariant Riemann structure is defined with respect to which ∇ is the Levi-Civita connection.

Słowa kluczowe

EN

Jordan-Banach algebras; JB*-triples; algebraic elements; Grassmann manifolds; Riemann manifolds; 17C27; 17C36; 17B65

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2005
• Tom: 3
• Numer: 2
• Strony: 188-202

Daty

wydano

2005-06-01

online

2005-06-01

Twórcy

autor

José Isidro

• Universidad de Santiago

Bibliografia

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Identyfikatory

DOI

10.2478/BF02479195