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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.
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.
Short geodesics of unitaries in the L2 metric
(Canadian Mathematical Soc, 2005-09)
Let M be a type II_1 von Neumann algebra, τ a trace in M, and l^2 (M,τ) the GNS Hilbert space of τ. We regard the unitary group U_M as a subset of l^2 (M,τ), and characterize the shortest smooth curves of unitaries joining ...
Weak Riemannian manifolds from finite index subfactors
(Springer, 2008-10)
Let N ⊂ M be a finite Jones' index inclusion of II1 factors and denote by UN ⊂ UM their unitary groups. In this article, we study the homogeneous space UM/UN, which is a (infinite dimensional) differentiable manifold, ...
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 ...
Geodesic neighborhoods in unitary orbits of self-adjoint operators of K + C
(Elsevier Science, 2021-08)
In the present paper, we study the unitary orbit of a compact Hermitian diagonal operator with spectral multiplicity one under the action of the unitary group U(K+C) of the unitization of the compact operators K(H) + C, ...
Metric geodesics of isometries in a Hilbert space and the extension problem
(American Mathematical Society, 2007-08)
We consider the problem of finding short smooth curves of isometries in a Hilbert space H. The length of a smooth curve γ(t), t ∈ [0, 1], is measured by means of ∫^1-0 γ^. (t)ǀǀ dt, where ǀǀ ǀǀ denotes the usual norm of ...
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 ...
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, ...
Codimension reduction in symmetric spaces
(Elsevier Science, 2014-05)
In this paper we give a short geometric proof of a generalization of a well-known result about reduction of codimension for submanifolds of Riemannian symmetric spaces