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

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dc.creatorIsidro, Jose M.
dc.date2001-10-30
dc.date.accessioned2026-07-07T04:44:08Z
dc.date.available2026-07-07T04:44:08Z
dc.descriptionGiven 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<r<\infty), G-invariant Riemann and Kähler structures are defined on M which in this way becomes a totally geodesic symmetric holomorphic manifold.
dc.description12 pages, Latex 2e, to appear
dc.identifierhttps://arxiv.org/abs/math/0110315
dc.identifierhttp://arxiv.org/abs/math/0110315
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/62517
dc.subjectFunctional Analysis
dc.subjectDifferential Geometry
dc.subject48G20, 72H51
dc.titleManifolds of algebraic elements in the algebra L(H) of bounded linear operators
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