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Spaces of nonpositive curvature arising from a finite algebra
(Elsevier, 2010-03)
In this paper we introduce a family of examples that can be regarded as spaces of nonpositive curvature, but with the distinct quality that they are not complete as metric spaces. This amounts to the fact that they are ...
A version of the Hermite--Hadamard inequality in a nonpositve curvature space
(Banach Mathematical Research Group, 2012-06)
We obtain some Hermite-Hadamard type inequalities for convex functions in a global non-positive curvature space.
Manifolds of semi-negative curvature
(Wiley, 2010-04)
This paper studies the metric structure of manifolds of semi-negative curvature. Explicit estimates on the geodesic distance and sectional curvature are obtained in the setting of homogeneous spaces G/K of Banach–Lie groups, ...
Nonpositively curved metric in the positive cone of a finite von Neumann algebra
(Oxford University Press, 2006-08)
In this paper we study the metric geometry of the space Σ of positive invertible elements of a von Neumann algebra. A with a finite, normal and faithful tracial state T. The trace induces an incomplete Riemannian metric ...
Nonpositive Curvature: A Geometric Approach to Hilbert-Schmidt Operators
(Elsevier Science, 2007-12)
We give a Riemannian structure to the set Σ of positive invertible unitized Hilbert–Schmidt operators, by means of the trace inner product. This metric makes of Σ a nonpositively curved, simply connected and metrically ...
Generalized small cancellation conditions, non-positive curvature and diagrammatic reducibility
(Royal Society of Edinburgh, 2021-03)
We present a metric condition which describes the geometry of classical small cancellation groups and applies also to other known classes of groups such as two-dimensional Artin groups. We prove that presentations satisfying ...
Nonpositive Curvature in p-Schatten class
(Elsevier, 2009-03-17)
We study the geometry of the set p, with 1 < p < ∞, which consists of perturbations of the identity operator by p-Schatten class operators, which are positive and invertible as elements of B(H). These manifolds have natural ...
Refinements of the Hermite–Hadamard Inequality in NPC Global Spaces
(De Gruyter, 2018-09-24)
In this paper we establish different refinements and applications of the Hermite-Hadamard inequality for convex functions in the context of NPC global spaces.
Unitarization of uniformly bounded subgroups in finite von Neumann algebras
(Oxford University Press, 2014-12)
This note presents a new proof of the fact that every uniformly bounded group of invertible elements in a finite von Neumann algebra is similar to a unitary group. In 1974, Vasilescu and Zsido proved this result using the ...
Lower Bound for the First Steklov Eigenvalue.
(2018-07-18)
In this paper we find lower bounds for the first Steklov eigenvalue in Riemannian
n-manifolds, n = 2, 3, with non-positive sectional curvature.