Completely isometric representations of $M_{cb}A(G)$ and $UCB(\hat G)^*$

@article{Neufang2008CompletelyIR,
  title={Completely isometric representations of \$M\_\{cb\}A(G)\$ and \$UCB(\hat G)^*\$},
  author={Matthias Neufang and Zhong‐Jin Ruan and Nico Spronk},
  journal={Transactions of the American Mathematical Society},
  year={2008},
  volume={360},
  pages={1133-1162}
}
. Let G be a locally compact group. It is shown that there exists a natural completely isometric representation of the completely bounded Fourier multiplier algebra M cb A ( G ), which is dual to the representation of the measure algebra M ( G ), on B ( L 2 ( G )). The image algebras of M ( G ) and M cb A ( G ) in CB σ ( B ( L 2 ( G ))) are intrinsically characterized, and some commutant theorems are proved. It is also shown that for any amenable group G , there is a natural completely… 
View via Publisher
ams.org
11 Citations

11 Citations

Completely bounded multipliers over locally compact quantum groups

In this paper, we consider several interesting multiplier algebras associated with a locally compact quantum group G . Firstly, we study the completely bounded right multiplier algebra Mcbr(L1(G)) .…

Representing Multipliers of the Fourier Algebra on Non-Commutative L p Spaces

Abstract We show that the multiplier algebra of the Fourier algebra on a locally compact group $G$ can be isometrically represented on a direct sum on non-commutative ${{L}^{p}}$ spaces associated…

Geometry of C⁎-algebras, and the bidual of their projective tensor product

A Non-commutative Fejér Theorem for Crossed Products, the Approximation Property, and Applications

We prove that a locally compact group has the approximation property (AP), introduced by Haagerup-Kraus, if and only if a non-commutative Fej\'{e}r theorem holds for the associated $C^*$- or von…

Realization of quantum group Poisson boundaries as crossed products

For a locally compact quantum group G , consider the convolution action of a quantum probability measure μ on L∞(G) . As shown by Junge–Neufang–Ruan, this action has a natural extension to a Markov…

THE OPERATOR SHIFT SPACE

  • T. Oikhberg
  • Mathematics
    Proceedings of the Edinburgh Mathematical Society
  • 2008
Abstract We construct and examine an operator space $X$, isometric to $\ell_2$, such that every completely bounded map from its subspace $Y$ into $X$ is a compact perturbation of a linear combination…

Representation of left centralizers for actions of locally compact quantum groups

We generalize the representation theorem of Junge, Neufang and Ruan [A representation theorem for locally compact quantum groups, Internat. J. Math. 20(3) (2009) 377-400], and some of the important…

Convolution of Trace Class Operators over Locally Compact Quantum Groups

Abstract We study locally compact quantum groups $\mathbb{G}$ through the convolution algebras ${{L}_{1}}\left( \mathbb{G} \right)$ and $\left( T\left( {{L}_{2}}\left( \mathbb{G} \right)…

Completely bounded maps and invariant subspaces

We provide a description of certain invariance properties of completely bounded bimodule maps in terms of their symbols. If $$\mathbb {G}$$ G is a locally compact quantum group, we characterise the…

First version Bimodules over VN ( G ) , harmonic operators and the non-commutative Poisson boundary

  • Mathematics

References

SHOWING 1-10 OF 48 REFERENCES

Isometric representation of M(G) on B(H)

In a recent paper, E. Størmer, among other things, proves the existence of an isometric isomorphism from the measure algebra M(G) of a locally compact abelian group G into BB(L2(G)), ([6],…

Isometric isomorphisms between Banach algebras related to locally compact groups

Let G1, G2 be locally compact groups. We prove in this paper that if T is an isometric isomorphism from the Banach algebra LUC(G1) * (the continuous dual of the Banach space of left uniformly…

Approximation properties for group *-algebras and group von Neumann algebras

Let G be a locally compact group, let C,' (G) (resp. VN(G)) be the C*-algebra (resp. the von Neumann algebra) associated with the left regular representation I of G, let A(G) be the Fourier algebra…

Measurable Schur Multipliers and Completely Bounded Multipliers of the Fourier Algebras

Let G be a locally compact group, Lp(G) be the usual Lp‐space for 1 ⩽ p ⩽ ∞, and A(G) be the Fourier algebra of G. Our goal is to study, in a new abstract context, the completely bounded multipliers…

Weakly almost periodic and uniformly continuous functionals on the Fourier algebra of any locally compact group

We define for any locally compact group G, the space of bounded uniformly continuous functionals on f, UCB(6), in the context of P. Eymard [Bull. Soc. Math. France 92 (1964), 181-236. MR 37 #42081…

Uniformly continuous functionals on the Fourier algebra of any locally compact group

Let G be any locally compact group. Let VN(G) be the von Neumann algebra generated by the left regular representation of G. We study in this paper the closed subspace UBC(G) of VN(G) consisting of…

On completely bounded bimodule maps over W$^*$-algebras

It is proved that for a von Neumann algebra A B(H) the subspace of normal maps is dense in the space of all completely bounded A-bimodule homomorphisms of B(H) in the point norm topology if and only…

The similarity degree of an operator algebra

. Let A be a unital operator algebra. Let us assume that every bounded unital homomorphism u : A → B ( H ) is similar to a contractive one. Let Sim( u ) = inf {k S k k S − 1 k} where the infimum runs…

Multipliers and modulus on Banach algebras related to locally compact groups

Abstract Let G be a locally compact group. In this paper we study moduli of products of elements and of multipliers of Banach algebras which are related to locally compact groups and which admit…

Left centralizers and isomorphisms of group algebras

The principal result (Theorem 1) of Part I states that, conversely, every left centralizer is a convolution with a regular measure. Important auxiliary theorems (3 and 4) furnish a characterization…