Geometrical significance
of the Löwner-Heinz inequality
Authors:
E. Andruchow, G. Corach and D. Stojanoff
Journal:
Proc. Amer. Math. Soc. 128 (2000), 1031-1037
MSC (1991):
Primary 46L05, 58B20
DOI:
https://doi.org/10.1090/S0002-9939-99-05085-6
Published electronically:
July 28, 1999
MathSciNet review:
1636922
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: It is proven that the Löwner-Heinz inequality , valid for all positive invertible operators
on the Hilbert space
and
, has equivalent forms related to the Finsler structure of the space of positive invertible elements of
or, more generally, of a unital
-algebra. In particular, the Löwner-Heinz inequality is equivalent to some type of ``nonpositive curvature" property of that space.
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Additional Information
E. Andruchow
Affiliation:
Instituto de Ciencias, Universidad Nacional de General Sarmiento, Roca 850, 1663-San Miguel, Argentina
Email:
eandruch@mate.dm.uba.ar
G. Corach
Affiliation:
Departamento de Matemática, Facultad de Ciencias Exactas, Ciudad Universitaria, 1428-Buenos Aires, Argentina
Email:
gcorach@mate.dm.uba.ar
D. Stojanoff
Affiliation:
Instituto Argentino de Matemática, Saavedra 15, 1083-Buenos Aires, Argentina
Email:
demetrio@mate.dm.uba.ar
DOI:
https://doi.org/10.1090/S0002-9939-99-05085-6
Received by editor(s):
May 29, 1997
Received by editor(s) in revised form:
May 18, 1998
Published electronically:
July 28, 1999
Additional Notes:
The authors were partially supported by UBACYT EX 261, PIP CONICET 4463/96 and PICT 2259 ANPCYT (Argentina)
Dedicated:
Dedicated to Mischa Cotlar, with affection and admiration, on his 86th anniversary
Communicated by:
David R. Larson
Article copyright:
© Copyright 2000
American Mathematical Society