Disjoint hypercyclic weighted translations on locally compact hausdorff spaces

2019 ◽  
Vol 69 (3) ◽  
pp. 647-664
Author(s):  
Ya Wang ◽  
Ze-Hua Zhou
Keyword(s):  
Borel Measure ◽  
Hausdorff Space ◽  
Weighted Space ◽  
Hausdorff Spaces ◽  
Locally Compact ◽  
Injective Mapping ◽  
Regular Borel Measure ◽  
Disjoint Hypercyclicity

Abstract Let G be a locally compact second countable Hausdorff space with a positive regular Borel measure λ, where λ is invariant under a continuous injective mapping φ : G → G. We characterize the disjoint hypercyclicity of finite weighted translations generated by φ acting on the weighted space Lp(G, ω) (1 ≤ p < ∞).

On the Ideal-Triangularizability of Semigroups of Quasinilpotent Positive Operators on C(K)

1998 ◽  
Vol 41 (3) ◽  
pp. 298-305
Author(s):  
M. T. Jahandideh
Keyword(s):  
Banach Lattice ◽  
Compact Hausdorff Space ◽  
Borel Measure ◽  
Hausdorff Space ◽  
Lower Semicontinuous ◽  
Integral Operators ◽  
Positive Operators ◽  
Locally Compact ◽  
Regular Borel Measure ◽  
The Ideal

AbstractIt is known that a semigroup of quasinilpotent integral operators, with positive lower semicontinuous kernels, on L2(X, μ), where X is a locally compact Hausdorff-Lindelöf space and μ is a σ-finite regular Borel measure on X, is triangularizable. In this article we use the Banach lattice version of triangularizability to establish the ideal-triangularizability of a semigroup of positive quasinilpotent integral operators on C(K) where K is a compact Hausdorff space.

scholarly journals Causal variational principles in the σ-locally compact setting: Existence of minimizers

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Felix Finster ◽  
Christoph Langer
Keyword(s):  
Borel Measure ◽  
Variational Principles ◽  
Hausdorff Spaces ◽  
Lagrange Equations ◽  
Locally Compact ◽  
Compact Range ◽  
Existence Of Minimizers ◽  
Lower Semi ◽  
Regular Borel Measure ◽  
Compact Subsets

AbstractWe prove the existence of minimizers of causal variational principles on second countable, locally compact Hausdorff spaces. Moreover, the corresponding Euler–Lagrange equations are derived. The method is to first prove the existence of minimizers of the causal variational principle restricted to compact subsets for a lower semi-continuous Lagrangian. Exhausting the underlying topological space by compact subsets and rescaling the corresponding minimizers, we obtain a sequence which converges vaguely to a regular Borel measure of possibly infinite total volume. It is shown that, for continuous Lagrangians of compact range, this measure solves the Euler–Lagrange equations. Furthermore, we prove that the constructed measure is a minimizer under variations of compact support. Under additional assumptions, it is proven that this measure is a minimizer under variations of finite volume. We finally extend our results to continuous Lagrangians decaying in entropy.

scholarly journals On the Fundamental Existence Theorem of Kishi

1963 ◽  
Vol 23 ◽  
pp. 189-198 ◽  
Author(s):  
Mitsuru Nakai
Keyword(s):  
Product Space ◽  
Borel Measure ◽  
Hausdorff Space ◽  
Lower Semicontinuous ◽  
Lower Semicontinuous Function ◽  
Semicontinuous Function ◽  
Locally Compact ◽  
Regular Borel Measure ◽  
Locally Compact Hausdorff Space ◽  
Semicontinuous Functions

Let Ω be a locally compact Hausdorff space and G(x, y) be a strictly positive lower semicontinuous function on the product space Ω×Ω of Ω. Such a function G(x, y) is called a kernel on Ω. The adjoint kernel Ğ(x, y) of G(x, y) is defined by Ğ(x, y) =G(y, x). Whenever we say a measure on Ω, we mean a positive regular Borel measure on Ω. The potential Gμ(x) and the adjoint potential Ğμ(x) of a measure μ relative to the kernel G(x, y) is defined byrespectively. These are also strictly positive lower semicontinuous functions on Ω provided μ≠0.

Spaces which Cannot be Written as a Countable Disjoint Union of Closed Subsets

1973 ◽  
Vol 16 (3) ◽  
pp. 435-437 ◽  
Author(s):  
C. Eberhart ◽  
J. B. Fugate ◽  
L. Mohler
Keyword(s):  
Hausdorff Space ◽  
Disjoint Union ◽  
Hausdorff Spaces ◽  
Locally Compact ◽  
The One ◽  
One Point Compactification ◽  
Compact Subsets

It is well known (see [3](1)) that no continuum (i.e. compact, connected, Hausdorff space) can be written as a countable disjoint union of its (nonvoid) closed subsets. This result can be generalized in two ways into the setting of locally compact, connected, Hausdorff spaces. Using the one point compactification of a locally compact, connected, Hausdorff space X one can easily show that X cannot be written as a countable disjoint union of compact subsets. If one makes the further assumption that X is locally connected, then one can show that X cannot be written as a countable disjoint union of closed subsets.(2)

Simple Links in Locally Compact Connected Hausdorff Spaces are Nondegenerate

1981 ◽  
Vol 34 (2) ◽  
pp. 349-355
Author(s):  
David John
Keyword(s):  
Hausdorff Space ◽  
Metric Spaces ◽  
Connected Space ◽  
Hausdorff Spaces ◽  
Locally Compact ◽  
Peano Continua

The fact that simple links in locally compact connected metric spaces are nondegenerate was probably first established by C. Kuratowski and G. T. Whyburn in [2], where it is proved for Peano continua. J. L. Kelley in [3] established it for arbitrary metric continua, and A. D. Wallace extended the theorem to Hausdorff continua in [4]. In [1], B. Lehman proved this theorem for locally compact, locally connected Hausdorff spaces. We will show that the locally connected property is not necessary.A continuum is a compact connected Hausdorff space. For any two points a and b of a connected space M, E(a, b) denotes the set of all points of M which separate a from b in M. The interval ab of M is the set E(a, b) ∪ {a, b}.

A Measure Theoretical Version of the Aleksandrov Theorem

2008 ◽  
Vol 15 (1) ◽  
pp. 53-61
Author(s):  
Majid Gazor
Keyword(s):  
Borel Measure ◽  
Measure Theory ◽  
Ordinal Number ◽  
Hausdorff Spaces ◽  
Locally Compact ◽  
Closed Sets

Abstract In this paper a theorem analogous to the Aleksandrov theorem is presented in terms of measure theory. Furthermore, we introduce the condensation rank of Hausdorff spaces and prove that any ordinal number is associated with the condensation rank of an appropriate locally compact totally imperfect space. This space is equipped with a probability Borel measure which is outer regular, vanishes at singletons, and is also inner regular in the sense of closed sets.

scholarly journals On projective lift and orbit spaces

1994 ◽  
Vol 50 (3) ◽  
pp. 445-449 ◽  
Author(s):  
T.K. Das
Keyword(s):  
Compact Hausdorff Space ◽  
Hausdorff Space ◽  
Covariant Functor ◽  
Hausdorff Spaces ◽  
Orbit Spaces ◽  
Locally Compact ◽  
Discontinuous Group ◽  
Coreflective Subcategory ◽  
Group Of Homeomorphisms ◽  
Locally Compact Hausdorff Space

By constructing the projective lift of a dp-epimorphism, we find a covariant functor E from the category Cd of regular Hausdorff spaces and continuous dp-epimorphisms to its coreflective subcategory εd consisting of projective objects of Cd We use E to show that E(X/G) is homeomorphic to EX/G whenever G is a properly discontinuous group of homeomorphisms of a locally compact Hausdorff space X and X/G is an object of Cd.

scholarly journals On dimension andweight of a local contact algebra

Filomat ◽  
2018 ◽  
Vol 32 (15) ◽  
pp. 5481-5500
Author(s):  
G. Dimov ◽  
E. Ivanova-Dimova ◽  
I. Düntsch
Keyword(s):  
Compact Hausdorff Space ◽  
Hausdorff Space ◽  
Hausdorff Spaces ◽  
Locally Compact ◽  
Local Contact ◽  
Continuous Maps ◽  
Contact Algebra ◽  
Contact Algebras ◽  
Locally Compact Hausdorff Space

As proved in [16], there exists a duality ?t between the category HLC of locally compact Hausdorff spaces and continuous maps, and the category DHLC of complete local contact algebras and appropriate morphisms between them. In this paper, we introduce the notions of weight wa and of dimension dima of a local contact algebra, and we prove that if X is a locally compact Hausdorff space then w(X) = wa(?t(X)), and if, in addition, X is normal, then dim(X) = dima(?t(X)).

On r*-Invariant Measure on a Locally Compact Semigroup with Recurrence

1980 ◽  
Vol 23 (2) ◽  
pp. 237-239
Author(s):  
Samuel Bourne
Keyword(s):  
Invariant Measure ◽  
Borel Measure ◽  
Compact Semigroup ◽  
Locally Compact ◽  
Borel Sets ◽  
Left Group ◽  
Locally Compact Semigroup ◽  
Regular Borel Measure

A regular Borel measure μ is said to be r*-invariant on a locally compact semigroup if μ(Ba-1) = μ(B) for all Borel sets B and points a of S, where Ba-1 ={xϵS, xaϵB}. In [1] Argabright conjectured that the support of an r*-invariant measure on a locally compact semigroup is a left group, Mukherjea and Tserpes [4] proved this conjecture in the case that the measure is finite; however their method of proof fails when the measure is infinite.

LOCALLY COMPACT GROUPS ADMITTING FAITHFUL STRONGLY CHAOTIC ACTIONS ON HAUSDORFF SPACES

2013 ◽  
Vol 23 (09) ◽  
pp. 1350158 ◽  
Author(s):  
FRIEDRICH MARTIN SCHNEIDER ◽  
SEBASTIAN KERKHOFF ◽  
MIKE BEHRISCH ◽  
STEFAN SIEGMUND
Keyword(s):  
Hausdorff Space ◽  
Geometric Characterization ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Topological Groups ◽  
Hausdorff Spaces ◽  
Locally Compact ◽  
Continuous Action

In this paper we provide a geometric characterization of those locally compact Hausdorff topological groups which admit a faithful strongly chaotic continuous action on some Hausdorff space.

Sign in / Sign up

Export Citation Format

Share Document