A Duality of Locally Compact Groups That Does Not Involve the Haar Measure
نویسندگان
چکیده
منابع مشابه
The Haar measure on some locally compact quantum groups
A locally compact quantum group is a pair (A,Φ) of a C-algebra A and a -homomorphism Φ from A to the multiplier algebra M(A ⊗ A) of the minimal C-tensor product A ⊗ A satisfying certain assumptions (see [K-V1] and [K-V2]). One of the assumptions is the existence of the Haar weights. These are densely defined, lower semi-continuous faithful KMS-weights satisfying the correct invariance propertie...
متن کاملHaar Measure for Compact Right Topological Groups
Compact right topological groups arise in topological dynamics and in other settings. Following H. Furstenberg's seminal work on distal flows, R. Ellis and I. Namioka have shown that the compact right topological groups of dynamical type always admit a probability measure invariant under the continuous left translations; however, this invariance property is insufficient to identify a unique pro...
متن کاملAn elementary approach to Haar integration and Pontryagin duality in locally compact abelian groups
We offer an elementary proof of Pontryagin duality theorem for compact and discrete abelian groups. To this end we make use of an elementary proof of Peter-Weyl theorem due to Prodanov that makes no recourse to Haar integral. As a long series of applications of this approach we obtain proofs of Bohr von Neumann’s theorem on almost periodic functions, Comfort-Ross’ theorem on the description of ...
متن کاملThe associated measure on locally compact cocommutative KPC-hypergroups
We study harmonic analysis on cocommutative KPC-hyper-groups, which is a generalization of DJS-hypergroups, introduced by Kalyuzhnyi, Podkolzin and Chapovsky. We prove that there is a relationship between the associated measures $mu$ and $gamma mu$, where $mu$ is a Radon measure on KPC-hypergroup $Q$ and $gamma$ is a character on $Q$.
متن کاملOn component extensions locally compact abelian groups
Let $pounds$ be the category of locally compact abelian groups and $A,Cin pounds$. In this paper, we define component extensions of $A$ by $C$ and show that the set of all component extensions of $A$ by $C$ forms a subgroup of $Ext(C,A)$ whenever $A$ is a connected group. We establish conditions under which the component extensions split and determine LCA groups which are component projective. ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: MATHEMATICA SCANDINAVICA
سال: 2015
ISSN: 1903-1807,0025-5521
DOI: 10.7146/math.scand.a-21162