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Banach manifolds of algebraic elements in the algebra (H) of bounded linear operatorsof bounded linear operators

José Isidro (2005)

Open Mathematics

Given a complex Hilbert space H, we study the manifold 𝒜 of algebraic elements in Z = H . We represent 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...

Bayoumi Quasi-Differential is different from Fréchet-Differential

Aboubakr Bayoumi (2006)

Open Mathematics

We prove that the Quasi Differential of Bayoumi of maps between locally bounded F-spaces may not be Fréchet-Differential and vice versa. So a new concept has been discovered with rich applications (see [1–6]). Our F-spaces here are not necessarily locally convex

Bounded cohomology and isometry groups of hyperbolic spaces

Ursula Hamenstädt (2008)

Journal of the European Mathematical Society

Let X be an arbitrary hyperbolic geodesic metric space and let Γ be a countable subgroup of the isometry group Iso ( X ) of X . We show that if Γ is non-elementary and weakly acylindrical (this is a weak properness condition) then the second bounded cohomology groups H b 2 ( Γ , ) , H b 2 ( Γ , p ( Γ ) ) ( 1 < ...

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