# Banach manifolds of algebraic elements in the algebra $\mathcal{L}$ (H) of bounded linear operatorsof bounded linear operators

Open Mathematics (2005)

- Volume: 3, Issue: 2, page 188-202
- ISSN: 2391-5455

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topJosé Isidro. "Banach manifolds of algebraic elements in the algebra \[\mathcal {L}\] (H) of bounded linear operatorsof bounded linear operators." Open Mathematics 3.2 (2005): 188-202. <http://eudml.org/doc/268863>.

@article{JoséIsidro2005,

abstract = {Given a complex Hilbert space H, we study the manifold \[\mathcal \{A\}\]
of algebraic elements in \[Z = \mathcal \{L\}\left( H \right)\]
. We represent \[\mathcal \{A\}\]
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 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.},

author = {José Isidro},

journal = {Open Mathematics},

keywords = {17C27; 17C36; 17B65},

language = {eng},

number = {2},

pages = {188-202},

title = {Banach manifolds of algebraic elements in the algebra \[\mathcal \{L\}\] (H) of bounded linear operatorsof bounded linear operators},

url = {http://eudml.org/doc/268863},

volume = {3},

year = {2005},

}

TY - JOUR

AU - José Isidro

TI - Banach manifolds of algebraic elements in the algebra \[\mathcal {L}\] (H) of bounded linear operatorsof bounded linear operators

JO - Open Mathematics

PY - 2005

VL - 3

IS - 2

SP - 188

EP - 202

AB - Given a complex Hilbert space H, we study the manifold \[\mathcal {A}\]
of algebraic elements in \[Z = \mathcal {L}\left( H \right)\]
. We represent \[\mathcal {A}\]
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 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.

LA - eng

KW - 17C27; 17C36; 17B65

UR - http://eudml.org/doc/268863

ER -

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