Manifolds of algebraic elements in the algebra L(H) of bounded linear operators

Details Manifolds of algebraic elements in the algebra L(H) of bounded linear operators Manifolds of algebraic elements in the algebra L(H) of bounded linear operators

2001-10-30

arxiv.org/abs/math/0110315v1

Mathematics

Functional Analysis

12 pages, Latex 2e, to appear

Scientific paper

Given a complex Hilbert space H, we study the differential geometry of the manifold A of normal algebraic elements in Z=L(H), the algebra of bounded linear operators on H. We represent A as a disjoint union of subsets M of Z and, using the algebraic structure of Z, a torsionfree affine connection $\nabla$ (that is invariant under the group G= Aut (Z) of automorphisms of Z) is defined on each of these connected components and the geodesics are computed. In case M consists of elements that have a fixed finite rank r, (0

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