Geometry of unitaries in a finite algebra: variation formulas and convexity
Given a C∗-algebra A with trace τ, we compute the first and second variation formulas for the p-energy functional Fp of the unitary group UA of A, for p = 2n an even integer, namely: Fp(γ) = Z b a τ([ ˙γ∗γ˙ ] n)dt, where γ(t) ∈ UA is a smooth curve for t ∈ [a, b]. As an application of these formulas...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2008 |
| País: | Argentina |
| Institución: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/19467 |
| Acceso en línea: | http://hdl.handle.net/11336/19467 |
| Access Level: | acceso abierto |
| Palabra clave: | Unitary Operator Convexity https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Sumario: | Given a C∗-algebra A with trace τ, we compute the first and second variation formulas for the p-energy functional Fp of the unitary group UA of A, for p = 2n an even integer, namely: Fp(γ) = Z b a τ([ ˙γ∗γ˙ ] n)dt, where γ(t) ∈ UA is a smooth curve for t ∈ [a, b]. As an application of these formulas, we prove that if dp denotes the geodesic distance of the Finsler metric induced by the p-norm xp = τ([x∗x] n)1/p, u0, u1, u2 ∈ UA with ui − uj < 1 2 p2 − √2 and δ(t) is a geodesic of UA joining δ(0) = u0 and δ(1) = u1, then the mapping f(t) = dp(u2, δ(t))p, t ∈ [0, 1] 15 is convex. |
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