GEOMETRY OF UNITARIES IN A FINITE ALGEBRA: VARIATION FORMULAS AND CONVEXITY
2008 ◽
Vol 19
(10)
◽
pp. 1223-1246
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Keyword(s):
Given a C*-algebra [Formula: see text] with trace τ, we compute the first and second variation formulas for the p-energy functional Fp 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 dp 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) = u0 and δ(1) = u1, then the mapping [Formula: see text] is convex.
2009 ◽
Vol 146
(2)
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pp. 435-459
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1993 ◽
Vol 04
(02)
◽
pp. 193-202
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2010 ◽
Vol 24
(05)
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pp. 587-597
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2003 ◽
Vol 24
(01)
◽
pp. 115-122
1982 ◽
Vol 91
(3)
◽
pp. 441-452
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Keyword(s):
2005 ◽
Vol 16
(09)
◽
pp. 1017-1031
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2003 ◽
Vol 7
(4)
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pp. 641-655
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