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A fixed point theorem and a norm inequality for operator means

โœ Scribed by Jaspal Singh Aujla

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
304 KB
Volume
290
Category
Article
ISSN
0024-3795

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โœฆ Synopsis

There is one to one correspondence between positive operator monotone functions on (0, w) and operator connections. For a symmetric connection a, it is proved that the map X --+ (AaX)aยฑ(BaX) from positive operators on a Hilbert space to itself, has a unique fixed point. Here a ยฑ denotes the dual of ~r. It is also proved that IhAaB[I ] ~< ]IIAII[ cr IUBIll for all unitarily invariant norms II1" Ill and for all positive operators A,B.

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