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.
@article{bwmeta1.element.doi-10_2478_BF02479195,
author = {Jos\'e Isidro},
title = {Banach manifolds of algebraic elements in the algebra \[\mathcal {L}\]
(H) of bounded linear operatorsof bounded linear operators},
journal = {Open Mathematics},
volume = {3},
year = {2005},
pages = {188-202},
zbl = {1124.58003},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_BF02479195}
}
José Isidro. Banach manifolds of algebraic elements in the algebra \[\mathcal {L}\]
(H) of bounded linear operatorsof bounded linear operators. Open Mathematics, Tome 3 (2005) pp. 188-202. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_BF02479195/
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