Wyniki wyszukiwania

1

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

100%

Isidro J.

Open Mathematics

|

2007

|

tom 5

|

nr 3

512-522

EN

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

2

On the Lie algebra of holomorphic infinitesimal isometries of some classical complex symmetric Banach manifolds

100%

Isidro J.

Open Mathematics

|

2007

|

tom 5

|

nr 4

696-709

EN

The Banach-Lie algebras ℌκ of all holomorphic infinitesimal isometries of the classical symmetric complex Banach manifolds of compact type (κ = 1) and non compact type (κ = −1) associated with a complex JB*-triple Z are considered and the Lie ideal structure of ℌκ is studied.

3

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

100%

Isidro J.

Open Mathematics

|

2005

|

tom 3

|

nr 2

188-202

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.

Ograniczanie wyników

3 Open Mathematics

3 Isidro J.

2 2007

1 2005

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

On the Lie algebra of holomorphic infinitesimal isometries of some classical complex symmetric Banach manifolds

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