scholarly journals A generalized type semigroup and dynamical comparison

2020 ◽  
pp. 1-18
Author(s):  
XIN MA
Keyword(s):  
Dynamical Systems ◽  
Compact Hausdorff Space ◽  
Discrete Group ◽  
Hausdorff Space ◽  
Countable Discrete Group ◽  
Higher Dimensional ◽  
Definition Of ◽  
Generalized Type

In this paper, we construct and study a semigroup associated to an action of a countable discrete group on a compact Hausdorff space that can be regarded as a higher dimensional generalization of the type semigroup. We study when this semigroup is almost unperforated. This leads to a new characterization of dynamical comparison and thus answers a question of Kerr and Schafhauser. In addition, this paper suggests a definition of comparison for dynamical systems in which neither the acting group is necessarily amenable nor the action is minimal.

scholarly journals Dynamical complexity and K-theory of Lp operator crossed products

2019 ◽  
pp. 1-33
Author(s):  
Yeong Chyuan Chung
Keyword(s):  
Compact Hausdorff Space ◽  
Discrete Group ◽  
Hausdorff Space ◽  
Crossed Products ◽  
Dynamical Complexity ◽  
Countable Discrete Group ◽  
K Theory ◽  
Assembly Map

We apply quantitative (or controlled) [Formula: see text]-theory to prove that a certain [Formula: see text] assembly map is an isomorphism for [Formula: see text] when an action of a countable discrete group [Formula: see text] on a compact Hausdorff space [Formula: see text] has finite dynamical complexity. When [Formula: see text], this is a model for the Baum–Connes assembly map for [Formula: see text] with coefficients in [Formula: see text], and was shown to be an isomorphism by Guentner et al.

scholarly journals Multipliers of Modules of Continuous Vector-Valued Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Liaqat Ali Khan ◽  
Saud M. Alsulami
Keyword(s):  
Compact Hausdorff Space ◽  
Hausdorff Space ◽  
Normed Spaces ◽  
Locally Compact ◽  
Continuous Vector ◽  
Vector Valued Functions ◽  
Vector Valued ◽  
Locally Compact Hausdorff Space ◽  
Locally Convex

In 1961, Wang showed that ifAis the commutativeC*-algebraC0(X)withXa locally compact Hausdorff space, thenM(C0(X))≅Cb(X). Later, this type of characterization of multipliers of spaces of continuous scalar-valued functions has also been generalized to algebras and modules of continuous vector-valued functions by several authors. In this paper, we obtain further extension of these results by showing thatHomC0(X,A)(C0(X,E),C0(X,F))≃Cs,b(X,HomA(E,F)),whereEandFarep-normed spaces which are also essential isometric leftA-modules withAbeing a certain commutativeF-algebra, not necessarily locally convex. Our results unify and extend several known results in the literature.

Property T and Amenable Transformation Group C*-algebras

2015 ◽  
Vol 58 (1) ◽  
pp. 110-114 ◽  
Author(s):  
F. Kamalov
Keyword(s):  
Compact Hausdorff Space ◽  
Discrete Group ◽  
Hausdorff Space ◽  
Transformation Group ◽  
Amenable Group ◽  
Transformation Groups ◽  
C Algebra ◽  
C Algebras ◽  
Property T ◽  
Tracial States

AbstractIt is well known that a discrete group that is both amenable and has Kazhdan’s Property T must be finite. In this note we generalize this statement to the case of transformation groups. We show that if G is a discrete amenable group acting on a compact Hausdorff space X, then the transformation group C*-algebra C*(X; G) has Property T if and only if both X and G are finite. Our approach does not rely on the use of tracial states on C*(X; G).

Property T for general C*-algebras

2013 ◽  
Vol 156 (2) ◽  
pp. 229-239 ◽  
Author(s):  
CHI–KEUNG NG
Keyword(s):  
Compact Hausdorff Space ◽  
Hausdorff Space ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Locally Compact ◽  
C Algebras ◽  
Strong Property ◽  
Property T ◽  
Definition Of ◽  
Locally Compact Hausdorff Space

AbstractIn this paper, we extend the definition of property T and strong property T to general C*-algebras (not necessarily unital). We show that if an inclusion pair of locally compact groups (G,H) has property T, then (C*(G), C*(H)) has property T. As a partial converse, if T is abelian and C*(G) has property T, then T is compact. We also show that if Ω is a first countable locally compact Hausdorff space, then C0(Ω) has (strong) property T if and only if Ω is discrete. Furthermore, the non-unital C*-algebra $c_0(\mathbb{Z}^n)\rtimes SL_n(\mathbb{Z})$ has strong property T when n ≥ 3. We also give some equivalent forms of strong property T, which are new even in the unital case.

scholarly journals PRYM VARIETIES AND THE INFINITE GRASSMANNIAN

1998 ◽  
Vol 09 (01) ◽  
pp. 75-93 ◽  
Author(s):  
FRANCISCO J. PLAZA MARTÍN
Keyword(s):  
Dynamical Systems ◽  
Moduli Space ◽  
Point Of View ◽  
Base Field ◽  
Prym Varieties ◽  
Arbitrary Base ◽  
Bkp Hierarchy ◽  
Definition Of

In this paper we study Prym varieties and their moduli space using the well-known techniques of the infinite Grassmannian. There are three main results of this paper: a new definition of the BKP hierarchy over an arbitrary base field (that generalizes the classical one over [Formula: see text]); a characterization of Prym varieties in terms of dynamical systems, and explicit equations for the moduli space of (certain) Prym varieties. For all of these problems the language of the infinte Grassmannian, in its algebro-geometric version, allows us to deal with these problems from the same point of view.

scholarly journals Duality properties of spaces of non-Archimedean valued functions

1987 ◽  
Vol 42 (1) ◽  
pp. 48-56
Author(s):  
W. Govaerts
Keyword(s):  
Uniform Convergence ◽  
Compact Hausdorff Space ◽  
Convex Space ◽  
Hausdorff Space ◽  
Continuous Functions ◽  
Complete Characterization ◽  
Bornological Space ◽  
Valued Field ◽  
Better Than

AbstractLet C(X, F) be the space of all continuous functions from the ultraregular compact Hausdorff space X into the separated locally K-convex space F; K is a complete, but not necessarily spherically complete, non-Archimedean valued field and C(X, F) is provided with the topology of uniform convergence on X We prove that C(X, F) is K-barrelled (respectively K-quasibarrelled) if and only if F is K-barrelled (respectively K-quasibarrelled) This is not true in the case of R or C-valued functions. No complete characterization of the K-bornological space C(X, F) is obtained, but our results are, nevertheless, slightly better than the Archimedean ones. Finally, we introduce a notion of K-ultrabornological spaces for K non-spherically complete and use it to study K-ultrabornological spaces C(X, F).

scholarly journals A note on nonfragmentability of Banach spaces

2001 ◽  
Vol 27 (1) ◽  
pp. 39-44
Author(s):  
S. Alireza Kamel Mirmostafaee
Keyword(s):  
Banach Spaces ◽  
Compact Hausdorff Space ◽  
Weak Topology ◽  
Hausdorff Space ◽  
Uniformly Convex ◽  
Completeness Property

We use Kenderov-Moors characterization of fragmentability to show that if a compact Hausdorff spaceXwith the tree-completeness property contains a disjoint sequences of clopen sets, then (C(X), weak) is not fragmented by any metric which is stronger than weak topology. In particular,C(X)does not admit any equivalent locally uniformly convex renorming.

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