scholarly journals Ergodic impulse control with constraint: locally compact case

2020 ◽  
Vol 122 ◽  
pp. 187-206
Author(s):  
Jose Luis Menaldi ◽  
Maurice Robin
Keyword(s):  
Impulse Control ◽  
Locally Compact ◽  
Compact Case

scholarly journals CONTINUOUS ASSOCIATION SCHEMES AND HYPERGROUPS

2018 ◽  
Vol 106 (03) ◽  
pp. 361-426
Author(s):  
MICHAEL VOIT
Keyword(s):  
Double Coset ◽  
Association Schemes ◽  
Stochastic Matrices ◽  
Locally Compact ◽  
Finite Dimensional ◽  
Infinite Case ◽  
Compact Case ◽  
Commutative Hypergroup ◽  
Double Coset Hypergroup ◽  
Discrete Hypergroups

Classical finite association schemes lead to finite-dimensional algebras which are generated by finitely many stochastic matrices. Moreover, there exist associated finite hypergroups. The notion of classical discrete association schemes can be easily extended to the possibly infinite case. Moreover, this notion can be relaxed slightly by using suitably deformed families of stochastic matrices by skipping the integrality conditions. This leads to a larger class of examples which are again associated with discrete hypergroups. In this paper we propose a topological generalization of association schemes by using a locally compact basis space $X$ and a family of Markov-kernels on $X$ indexed by some locally compact space $D$ where the supports of the associated probability measures satisfy some partition property. These objects, called continuous association schemes, will be related to hypergroup structures on $D$ . We study some basic results for this notion and present several classes of examples. It turns out that, for a given commutative hypergroup, the existence of a related continuous association scheme implies that the hypergroup has many features of a double coset hypergroup. We, in particular, show that commutative hypergroups, which are associated with commutative continuous association schemes, carry dual positive product formulas for the characters. On the other hand, we prove some rigidity results in particular in the compact case which say that for given spaces $X,D$ there are only a few continuous association schemes.

scholarly journals What is typical?

2011 ◽  
Vol 48 (A) ◽  
pp. 379-389 ◽  
Author(s):  
Günter Last ◽  
Hermann Thorisson
Keyword(s):  
Topological Group ◽  
Random Element ◽  
Random Measure ◽  
Measurable Space ◽  
Locally Compact ◽  
Recent Developments ◽  
Compact Case ◽  
Definition Of

Let ξ be a random measure on a locally compact second countable topological group, and letXbe a random element in a measurable space on which the group acts. In the compact case we give a natural definition of the concept that the origin is a typical location forXin the mass of ξ, and prove that when this holds, the same is true on sets placed uniformly at random around the origin. This new result motivates an extension of the concept of typicality to the locally compact case where it coincides with the concept of mass-stationarity. We describe recent developments in Palm theory where these ideas play a central role.

scholarly journals UNIVERSAL SUBGROUPS OF POLISH GROUPS

2014 ◽  
Vol 79 (4) ◽  
pp. 1148-1183 ◽  
Author(s):  
KONSTANTINOS A. BEROS
Keyword(s):  
Topological Group ◽  
Banach Spaces ◽  
Topological Groups ◽  
Locally Compact ◽  
Polish Groups ◽  
Countable Power ◽  
Compact Case ◽  
Image Position ◽  
The Relationship ◽  
Compactly Generated

AbstractGiven a class${\cal C}$of subgroups of a topological groupG, we say that a subgroup$H \in {\cal C}$is auniversal${\cal C}$subgroupofGif every subgroup$K \in {\cal C}$is a continuous homomorphic preimage ofH. Such subgroups may be regarded as complete members of${\cal C}$with respect to a natural preorder on the set of subgroups ofG. We show that for any locally compact Polish groupG, the countable powerGωhas a universalKσsubgroup and a universal compactly generated subgroup. We prove a weaker version of this in the nonlocally compact case and provide an example showing that this result cannot readily be improved. Additionally, we show that many standard Banach spaces (viewed as additive topological groups) have universalKσand compactly generated subgroups. As an aside, we explore the relationship between the classes ofKσand compactly generated subgroups and give conditions under which the two coincide.

scholarly journals Topological full groups of ample groupoids with applications to graph algebras

2019 ◽  
Vol 30 (04) ◽  
pp. 1950018 ◽  
Author(s):  
Petter Nyland ◽  
Eduard Ortega
Keyword(s):  
Embedding Theorem ◽  
Full Group ◽  
Graph Algebras ◽  
Graph Groupoids ◽  
Locally Compact ◽  
Abstract Group ◽  
Path Algebras ◽  
Compact Case ◽  
Leavitt Path Algebras ◽  
Definition Of

We study the topological full group of ample groupoids over locally compact spaces. We extend Matui’s definition of the topological full group from the compact to the locally compact case. We provide two general classes of étale groupoids for which the topological full group, as an abstract group, is a complete isomorphism invariant, hereby extending Matui’s Isomorphism Theorem. As an application, we study graph groupoids and their topological full groups, and obtain sharper results for this class. The machinery developed in this process is used to prove an embedding theorem for ample groupoids, akin to Kirchberg’s Embedding Theorem for [Formula: see text]-algebras. Consequences for graph [Formula: see text]-algebras and Leavitt path algebras are also spelled out. In particular, we improve on a recent embedding theorem of Brownlowe and Sørensen for Leavitt path algebras.

A Hilbert cube compactification of the function space with the compact-open topology

2009 ◽  
Vol 7 (4) ◽  
Author(s):  
Atsushi Kogasaka ◽  
Katsuro Sakai
Keyword(s):  
Closed Interval ◽  
Continuous Functions ◽  
Metrizable Space ◽  
Hilbert Cube ◽  
Compact Open Topology ◽  
Locally Compact ◽  
Closed Sets ◽  
Isolated Points ◽  
Compact Case ◽  
Separable Metrizable Space

AbstractLet X be an infinite, locally connected, locally compact separable metrizable space. The space C(X) of real-valued continuous functions defined on X with the compact-open topology is a separable Fréchet space, so it is homeomorphic to the psuedo-interior s = (−1, 1)ℕ of the Hilbert cube Q = [−1, 1]ℕ. In this paper, generalizing the Sakai-Uehara’s result to the non-compact case, we construct a natural compactification $$ \bar C $$(X) of C(X) such that the pair ($$ \bar C $$(X), C(X)) is homeomorphic to (Q, s). In case X has no isolated points, this compactification $$ \bar C $$(X) coincides with the space USCCF(X,) of all upper semi-continuous set-valued functions φ: X → = [−∞, ∞] such that each φ(x) is a closed interval, where the topology for USCCF(X, ) is inherited from the Fell hyperspace Cld*F(X × ) of all closed sets in X × .

scholarly journals What is typical?

2011 ◽  
Vol 48 (A) ◽  
pp. 379-389 ◽  
Author(s):  
Günter Last ◽  
Hermann Thorisson
Keyword(s):  
Topological Group ◽  
Random Element ◽  
Random Measure ◽  
Measurable Space ◽  
Locally Compact ◽  
Recent Developments ◽  
Compact Case ◽  
Definition Of

Let ξ be a random measure on a locally compact second countable topological group, and let X be a random element in a measurable space on which the group acts. In the compact case we give a natural definition of the concept that the origin is a typical location for X in the mass of ξ, and prove that when this holds, the same is true on sets placed uniformly at random around the origin. This new result motivates an extension of the concept of typicality to the locally compact case where it coincides with the concept of mass-stationarity. We describe recent developments in Palm theory where these ideas play a central role.

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