GEOMETRY OF UNITARIES IN A FINITE ALGEBRA: VARIATION FORMULAS AND CONVEXITY

Esteban Andruchow, Lázaro Recht

Type: Article

Publication Date: 2008-11-01

Citations: 14

DOI: https://doi.org/10.1142/s0129167x08005102

Abstract

Given a C*-algebra [Formula: see text] with trace τ, we compute the first and second variation formulas for the p-energy functional F p of the unitary group [Formula: see text] of [Formula: see text], for p = 2n an even integer, namely: [Formula: see text] where [Formula: see text] is a smooth curve for t ∈ [a, b]. As an application of these formulas, we prove that if d p denotes the geodesic distance of the Finsler metric induced by the p-norm [Formula: see text] with [Formula: see text] and δ(t) is a geodesic of [Formula: see text] joining δ(0) = u 0 and δ(1) = u 1 , then the mapping [Formula: see text] is convex.

Locations

International Journal of Mathematics - View
CONICET Digital (CONICET) - View - PDF

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