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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...

Holomorphic retractions and boundary Berezin transforms

Jonathan Arazy, Miroslav Engliš, Wilhelm Kaup (2009)

Annales de l’institut Fourier

In an earlier paper, the first two authors have shown that the convolution of a function f continuous on the closure of a Cartan domain and a K -invariant finite measure μ on that domain is again continuous on the closure, and, moreover, its restriction to any boundary face F depends only on the restriction of f to F and is equal to the convolution, in  F , of the latter restriction with some measure μ F on F uniquely determined by  μ . In this article, we give an explicit formula for μ F in terms of  F ,...

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