On the definition of real -algebras

We prove that, if is a real -algebra having a predual , then is the unique predual of and the product of is -continuous.

     

The singularH 2,2-invariant quartic surfaces in ℙ3

AnH _2,2-invariant quartic surface in ₃ is a quartic surface in ₃ invariant under the Heisenberg groupH _2,2 of level (2, 2), the family ofH _2,2-invariant quartic surfaces is parametrized by ₄. For each ₄, the corresponding quartic surfaceX will be a Kummer surface, ifX is singular. The equation for { = 0} ₄ parametrizing all Kummer surfaces is well known. We find another more symmetric form (with respect to a 5-dimensional representation of the symmetric group S₆) for this equation.The aim of this note is to describe all singularH _2,2-invariant quartic surfaces in ₃.     

Determining boundary sets of bounded symmetric domains

We consider bounded symmetric domains in complex Banach spaces. It is known that each of these domains can be realized as open unit ballD of a uniquely determined complex Banach spaceE and that every biholomorphic automorphismg ofD extends holomorphically to the closure ofD inE. We study subsetsS of (and in particular of the boundary ϖD) such that every automorphismg is already uniquely determined by its values onS. We also consider subsetsS with the analogue topological property: For every sequence (g _n ) of automorphisms converging uniformly onS tog the convergence is already uniform onD. Supported by Acción Integrada Hispano-Alemana Supported by Xunta de Galicia, project Xuga 20702 B 90     

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

The Banach-Lie algebras ℌ ^κ 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 ℌ ^κ is studied.      

Novel simple and highly modular ligands for efficient asymmetric transfer-hydrogenation of ketones

Novel simple and highly modular dipeptide-analogue ligands combined with [RuCl2(p-cymene)]2 were demonstrated to efficiently catalyze the reduction of ketones under hydrogen transfer conditions with enantioselectivities up to 96%.     

Weak continuity of holomorphic automorphisms in JB*-triples

Supported by DAAD grant 313, programm II (1991)     

Moduli space of potentials in the Aharonov-Bohm effect

We present a simplified derivation of the fact that the set of gauge equivalence classes or moduli space of flat connections (potentials) in the abelian Aharonov-Bohm effect, is isomorphic to the circle. The length of this circle is the absolute value of the electric charge.     

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

Given a complex Hilbert space H, we study the manifold of algebraic elements in . We represent 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. Supported by Ministerio de Educación y Cultura of Spain, Research Project BFM2002-01529.     

A Note on a Theorem of H. Cartan

We prove that if D C is a bounded domain with real analytic boundary, and D is either pseudoconvex or it satisfies condition (R), then the compact open topology in Aut(D), the group of holomorphic automorphisms of D is the topology of uniform convergence on D.