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Article
Embedding Locally Compact Semigroups into Groups
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Article
John A. Hildebrant (1935–2003)
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Article
Symmetric Sets With Midpoints and Algebraically Equivalent Theories
In this paper we consider an algebraic generalization of symmetric spaces of noncompact type to a more general class of symmetric structures equipped with midpoints. These symmetric structures are shown to hav...
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Article
The Symplectic Semigroup and Riccati Differential Equations
In this paper, we study close connections that exist between the Riccati operator (differential) equation that arises in linear control systems and the symplectic group and its subsemigroup of symplectic Hamil...
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Article
Semigroup closures of finite rank symmetric inverse semigroups
We introduce the notion of semigroup with a tight ideal series and investigate their closures in semitopological semigroups, particularly inverse semigroups with continuous inversion. As a corollary we show th...
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Article
Monotonic properties of the least squares mean
We settle an open problem of several years standing by showing that the least squares mean for positive definite matrices is monotone for the usual (Loewner) order. Indeed we show this is a special case of its...
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Article
A Lipschitz constant formula for vector addition in cones with applications to Stein-like equations
For a cone C equipped with the Thompson metric and \({a\in C}\) , we show that the translation map
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Article
Unit Balls, Lorentz Boosts, and Hyperbolic Geometry
The bounded symmetric spaces naturally associated with the Poincaré and Beltrami-Klein models of hyperbolic geometry on the open unit ball B in ...
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Chapter
Continuous and Completely Distributive Lattices
The study of continuous lattices was initiated by Dana Scott in the late 1960s in order to build mathematical models for certain constructs in theoretical computer science ([638] in LTF), and computational not...
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Article
On a subsemigroup of the universal covering of Lie semigroups
Let \(G\) G be ...
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Article
The Equivalence of QRB, QFS, and Compactness for Quasicontinuous Domains
In this article we show the equivalence of QRB, QFS, and compact quasicontinuous domains. QRB and QFS domains are generalizations of RB and FS domains to the setting of quasicontinuous domains and compactness ...
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Article
Continuity of Function Spaces from Pointwise Directed Families of Characteristic Functions
In earlier work the second author introduced the tool of pointwise directed families of characteristic functions to establish that certain continuous function spaces [X → Q] were continuous domains. In this paper...
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Article
Homotopy Path Spaces for Families of Admissible Paths
Motivated by the search for universal orbits in geometric control theory and universal topological semigroups over local semigroups in topological groups, particularly Lie groups, we introduce a very general a...
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Article
In memoriam: Klaus Keimel (1939–2017)
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Article
Loos symmetric cones
In this paper we consider Loos symmetric spaces on an open cone \(\Omega \) ...
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Article
Nonhomogeneous Karcher equations with vector fields on positive definite matrices
We study a family of Riemannian gradient equations on the Cartan–Hadamard–Riemannian manifold \({\mathbb P}_N\) ...
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Article
From hyperbolic geometry to \(2\times 2\) Hermitian matrices and back
In this paper we show how the space \(\mathbf {SPD}\) SPD of ...
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Article
Weighted Karcher means on unipotent Lie groups
A substantial theory of the Karcher mean exists in the settings of Riemannian manifolds and positive matrix and operator spaces. Here a general setting for the study of the Karcher mean on Lie groups is propos...
