The Experts below are selected from a list of 273 Experts worldwide ranked by ideXlab platform
Anthony To-ming Lau - One of the best experts on this subject based on the ideXlab platform.
-
the rajchman algebra b0 g of a Locally Compact Group g
Bulletin Des Sciences Mathematiques, 2016Co-Authors: Eberhard Kaniuth, Anthony To-ming Lau, A UlgerAbstract:Abstract Let G be a Locally Compact Group, B ( G ) the Fourier–Stieltjes algebra of G and B 0 ( G ) = B ( G ) ∩ C 0 ( G ) . The space B 0 ( G ) is a closed ideal of B ( G ) . In this paper, we study the Banach algebra B 0 ( G ) under various aspects. The main emphasis is on regularity and the existence of various kinds of approximate identities, the question of when the quotient of B 0 ( G ) modulo the Fourier algebra A ( G ) is radical, the Bochner–Schoenberg–Eberlein property and a characterization of elements in B 0 ( G ) in terms of continuity of translation properties. The paper also contains a number of illustrating examples.
-
weak fixed point property and asymptotic centre for the fourier stieltjes algebra of a Locally Compact Group
Journal of Functional Analysis, 2013Co-Authors: Gero Fendler, Anthony To-ming Lau, Michael LeinertAbstract:In this paper we show that the Fourier–Stieltjes algebra B(G) of a non-Compact Locally Compact Group G cannot have the weak⁎ fixed point property for nonexpansive mappings. This answers two open problems posed at a conference in Marseille-Luminy in 1989. We also show that a Locally Compact Group is Compact exactly if the asymptotic centre of any non-empty weak⁎ closed bounded convex subset C in B(G) with respect to a decreasing net of bounded subsets is a non-empty norm Compact subset. In particular, when G is Compact, B(G) has the weak⁎ fixed point property for left reversible semiGroups. This generalizes a classical result of T.C. Lim for the circle Group. As a consequence of our main results we obtain that a number of properties, some of which were known to hold for Compact Groups, in fact characterize Compact Groups.
-
Fixed point property and the Fourier algebra of a Locally Compact Group
Transactions of the American Mathematical Society, 2008Co-Authors: Anthony To-ming Lau, Michael LeinertAbstract:We establish some characterizations of the weak fixed point property (weak fpp) for noncommutative (and commutative) L 1 spaces and use this for the Fourier algebra A(G) of a Locally Compact Group G. In particular we show that if G is an IN-Group, then A(G) has the weak fpp if and only if G is Compact. We also show that if G is any Locally Compact Group, then A(G) has the fixed point property (fpp) if and only if G is finite. Furthermore if a nonzero closed ideal of A(G) has the fpp, then G must be discrete.
-
on hochschild cohomology of the augmentation ideal of a Locally Compact Group
Mathematical Proceedings of the Cambridge Philosophical Society, 1999Co-Authors: Niels Gronbaek, Anthony To-ming LauAbstract:In this paper we study the cohomology Groups H n ( I , I *) and H n ([Uscr ], [Uscr ]*) where [Uscr ] is a Banach algebra with a bounded approximate identity and I is a codimension one closed two-sided ideal of [Uscr ]. This is applied to the case when [Uscr ] is the Group algebra L 1 ( G ) of a Locally Compact Group G and I ={ f ∈ L 1 ( G )[mid ] ∫ G f =0}, the augmentation ideal of G . We show that if G is inner amenable, then I is always weakly amenable, i.e. [Hscr ] 1 ( I , I *)={0}.
-
ergodic sequences in the fourier stieltjes algebra and measure algebra of a Locally Compact Group
Transactions of the American Mathematical Society, 1999Co-Authors: Anthony To-ming Lau, Viktor LosertAbstract:Let G be a Locally Compact Group. Blum and Eisenberg proved that if G is abelian, then a sequence of probability measures on G is strongly ergodic if and only if the sequence converges weakly to the Haar measure on the Bohr Compactification of G. In this paper, we shall prove an extension of Blum and Eisenberg’s Theorem for ergodic sequences in the Fourier-Stieltjes algebra of G. We shall also give an improvement to Milnes and Paterson’s more recent generalization of Blum and Eisenberg’s result to general Locally Compact Groups, and we answer a question of theirs on the existence of strongly (or weakly) ergodic sequences of measures on G.
Alexander I Shtern - One of the best experts on this subject based on the ideXlab platform.
-
Continuity conditions for finite-dimensional representations of connected Locally Compact Groups
Russian Journal of Mathematical Physics, 2012Co-Authors: Alexander I ShternAbstract:We obtain simple necessary and sufficient conditions for the continuity of a Locally bounded finite-dimensional representation of a connected Locally Compact Group. We also prove that the discontinuity Group of a Locally bounded finite-dimensional representation of a connected Locally Compact Group is a central subGroup in the closure of the image.
-
The structure of homomorphisms of connected Locally Compact Groups into Compact Groups
Izvestiya: Mathematics, 2011Co-Authors: Alexander I ShternAbstract:We obtain consequences of the theorem concerning the automatic continuity of Locally bounded finite-dimensional representations of connected Lie Groups on the commutator subGroup of the Group and also of an analogue of Lie's theorem for (not necessarily continuous) finite-dimensional representations of soluble Lie Groups. In particular, we prove that an almost connected Locally Compact Group admitting a (not necessarily continuous) injective homomorphism into a Compact Group also admits a continuous injective homomorphism into a Compact Group, and thus the given Group is a finite extension of the direct product of a Compact Group and a vector Group. We solve the related problem of describing the images of (not necessarily continuous) homomorphisms of connected Locally Compact Groups into Compact Groups. Moreover, we refine the description of the von Neumann kernel of a connected Locally Compact Group and describe the intersection of the kernels of all (not necessarily continuous) finite-dimensional unitary representations of a given connected Locally Compact Group. Some applications are mentioned. We also show that every almost connected Locally Compact Group admitting a (not necessarily continuous) Locally bounded injective homomorphism into an amenable almost connected Locally Compact Group is amenable.
-
a criterion for a topological Group to admit a continuous embedding in a Locally Compact Group
Russian Journal of Mathematical Physics, 2008Co-Authors: Alexander I ShternAbstract:It is proved that a topological Group admits a continuous embedding in a Locally Compact Group if and only if the Group in question admits a separating family of unitary representations defining a symmetric Hopf-von Neumann algebra whose intrinsic Group coincides with the set of nonzero characters of the predual algebra.
-
a criterion for the second real continuous bounded cohomology of a Locally Compact Group to be finite dimensional
Acta Applicandae Mathematicae, 2001Co-Authors: Alexander I ShternAbstract:We present a brief review of the theory of quasi-characters and quasi-representations and prove a necessary and sufficient condition that the second real continuous bounded cohomology of a Locally Compact Group to be finite-dimensional. This criterion is established by using the properties of continuous pseudocharacters on a Locally Compact Group.
-
Structure Properties and Real Continuous Bounded 2-Cohomology of Locally Compact Groups
Functional Analysis and Its Applications, 2001Co-Authors: Alexander I ShternAbstract:With the help of some structure results for Locally Compact Groups, the second real continuous bounded cohomology Group of a connected Locally Compact Group is described and it is proved that the corresponding Group is finite-dimensional for any almost connected Locally Compact Group.
V Losert - One of the best experts on this subject based on the ideXlab platform.
-
the c algebra generated by operators with Compact support on a Locally Compact Group
Journal of Functional Analysis, 1993Co-Authors: Anthony To-ming Lau, V LosertAbstract:Abstract Let G be a Locally Compact Group and VN(G) be the von Neumann algebra generated by the left regular representation of G. Let UCB(Ĝ) denote the C*-subalgebra generated by operators in VN(G) with Compact support. When G is abelian, UCB(Ĝ) corresponds to the space of bounded uniformly continuous functions on the dual Group Ĝ of G. In this paper we prove among other things that for a large class of Locally Compact Groups which include the Heisenberg Group, the "ax + b" Group and the motion Group, the centre of the Banach algebra UCB(Ĝ)* is the Fourier Stieltjes algebra B(G).
Tianxuan Miao - One of the best experts on this subject based on the ideXlab platform.
-
Uniformly Continuous Functionals and M-Weakly Amenable Groups
Canadian Journal of Mathematics, 2013Co-Authors: Brian E. Forrest, Tianxuan MiaoAbstract:AbstractLet G be a Locally Compact Group. Let AM(G) (A0(G))denote the closure of A(G), the Fourier algebra of G in the space of bounded (completely bounded) multipliers of A(G). We call a Locally Compact Group M-weakly amenable if AM(G) has a bounded approximate identity. We will show that when G is M-weakly amenable, the algebras AM(G) and A0(G) have properties that are characteristic of the Fourier algebra of an amenable Group. Along the way we show that the sets of topologically invariant means associated with these algebras have the same cardinality as those of the Fourier algebra.
George A. Willis - One of the best experts on this subject based on the ideXlab platform.
-
Computing the Scale of an Endomorphism of a totally Disconnected Locally Compact Group
Axioms, 2017Co-Authors: George A. WillisAbstract:The scale of an endomorphism of a totally disconnected, Locally Compact Group G is defined and an example is presented which shows that the scale function is not always continuous with respect to the Braconnier topology on the automorphism Group of G. Methods for computing the scale, which is a positive integer, are surveyed and illustrated by applying them in diverse cases, including when G is Compact; an automorphism Group of a tree; Neretin’s Group of almost automorphisms of a tree; and a p-adic Lie Group. The information required to compute the scale is reviewed from the perspective of the, as yet incomplete, general theory of totally disconnected, Locally Compact Groups.
-
the nub of an automorphism of a totally disconnected Locally Compact Group
Ergodic Theory and Dynamical Systems, 2014Co-Authors: George A. WillisAbstract:To any automorphism, $\alpha $ , of a totally disconnected, Locally Compact Group, $G$ , there is associated a Compact, $\alpha $ -stable subGroup of $G$ , here called the nub of $\alpha $ , on which the action of $\alpha $ is ergodic. Ergodic actions of automorphisms of Compact Groups have been studied extensively in topological dynamics and results obtained transfer, via the nub, to the study of automorphisms of general Locally Compact Groups. A new proof that the contraction Group of $\alpha $ is dense in the nub is given, but it is seen that the two-sided contraction Group need not be dense. It is also shown that each pair $(G, \alpha )$ , with $G$ Compact and $\alpha $ ergodic, is an inverse limit of pairs that have ‘finite depth’ and that analogues of the Schreier refinement and Jordan–Holder theorems hold for pairs with finite depth.
-
the nub of an automorphism of a totally disconnected Locally Compact Group
arXiv: Group Theory, 2011Co-Authors: George A. WillisAbstract:To any automorphism, $\alpha$, of a totally disconnected, Locally Compact Group, $G$, there is associated a Compact, $\alpha$-stable subGroup of $G$, here called the \emph{nub} of $\alpha$, on which the action of $\alpha$ is topologically transitive. Topologically transitive actions of automorphisms of Compact Groups have been studied extensively in topological dynamics and results obtained transfer, via the nub, to the study of automorphisms of general Locally Compact Groups. A new proof that the contraction Group of $\alpha$ is dense in the nub is given, but it is seen that the two-sided contraction Group need not be dense. It is also shown that each pair $(G,\alpha)$, with $G$ Compact and $\alpha$ topologically transitive, is an inverse limit of pairs that have `finite depth' and that analogues of the Schreier Refinement and Jordan-H\"older Theorems hold for pairs with finite depth.
-
the direction of an automorphism of a totally disconnected Locally Compact Group
Mathematische Zeitschrift, 2006Co-Authors: Udo Baumgartner, George A. WillisAbstract:We describe the asymptotic behavior of automorphisms of totally disconnected Locally Compact Groups in terms of a set of `directions' which comes equipped with a natural pseudo-metric. The structure at infinity obtained by completing the induced metric quotient space of the set of directions recovers familiar objects such as: the set of ends of the tree for the Group of inner automorphisms of the Group of isometries of a regular Locally finite tree; and the spherical Bruhat-Tits building for the Group of inner automorphisms of the set of rational points of a semisimple Group over a local field.
