Artículo
Geometry of unitaries in a finite algebra: variation formulas and convexity
Fecha de publicación:
12/2008
Editorial:
World Scientific
Revista:
International Journal Of Mathematics
ISSN:
0129-167X
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Clasificación temática:
Resumen
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.
Palabras clave:
Unitary Operator
,
Convexity
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Articulos(IAM)
Articulos de INST.ARG.DE MATEMATICAS "ALBERTO CALDERON"
Articulos de INST.ARG.DE MATEMATICAS "ALBERTO CALDERON"
Citación
Andruchow, Esteban; Recht, Lázaro; Geometry of unitaries in a finite algebra: variation formulas and convexity; World Scientific; International Journal Of Mathematics; 19; 10; 12-2008; 1-24; 1223
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