On ideals in the bidual of the Fourier algebra and related algebras

Filali, M.; Neufang, Matthias; Monfared, M. Sangani

doi:10.1016/j.jfa.2009.12.011

Cited by 5 publications

(6 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Recall that T LC is the universal semigroup compactification of T in the locally compact case (see [3], Theorem 5.7 on page 173). This line of research has been pursued further by Filali, Pym and Salmi ( [14,15]), and analogous results have been obtained in a Fourier algebra setting by Filali, Neufang and Monfared ( [13]).…”

Section: Introductionmentioning

confidence: 70%

Multiple disjointness and invariant measures on minimal distal flows

Rautio

2015

Studia Math.

View full text Add to dashboard Cite

As the main theorem, it is proved that a collection of minimal P I-flows with a common phase group and satisfying a certain algebraic condition is multiply disjoint if and only if the collection of the associated maximal equicontinuous factors is multiply disjoint. In particular, this result holds for collections of minimal distal flows. The disjointness techniques are combined with Furstenberg's example of a minimal distal system with multiple invariant measures to find the exact cardinalities of (extreme) invariant means on D(Z) and D(R), the spaces of distal functions on Z and R, respectively. In all cases, this cardinality is 2 c . The size of the quotient of D(Z) or of D(R) by a closed subspace with a unique invariant mean is observed to be non-separable by applying the same ideas.2010 Mathematics Subject Classification. Primary 37B05; Secondary 43A60.

show abstract

Section: Introductionmentioning

confidence: 70%

Multiple disjointness and invariant measures on minimal distal flows

Rautio

2015

Studia Math.

View full text Add to dashboard Cite

show abstract

“…and A p (G) * * , Baker-Filali [3,4], Filali [13], Filali-Pym [16], and Filali-Salmi [17] for (among other things) X * , L 1 (G) * * , and LU C(G) * , where X is an introverted subspace of C(G), Derighetti et al [10] for duals of introverted subspaces of ppseudo measures P M p (G), and the most recent work by the present authors and Neufang [14] on A(G) * * and UC 2 (G) * . Let G be a locally compact group, 1 < p < ∞, and L (L p (G)) be the space of continuous linear operators on L p (G).…”

mentioning

confidence: 79%

“…Recently in [14] the present authors and M. Neufang proved the following theorem regarding left and right ideals in A(G) * * and in UC 2 (G) * . This result is proved in [14,Theorems 4.3,4.4].…”

mentioning

confidence: 84%

See 1 more Smart Citation

Finite-dimensional left ideals in the duals of introverted spaces

Filali

Monfared

2011

Proc. Amer. Math. Soc.

Self Cite

View full text Add to dashboard Cite

show abstract

“…However, the direct arguments we indicated there without detouring through quantum groups are much more natural and elementary. We also note that if m ∈ V N (G) * is a topological left invariant mean, then the 1-dimensional subspace m spanned by m is closed left ideal in the Banach algebra V N (G) * = A(G) * * with the Arens product (see [15,14] for the study of ideals in the bidual of A(G)).…”

Section: Finite Dimensional Invariant Subspacesmentioning

confidence: 99%

Finite-dimensional invariant subspace property and amenability for a class of Banach algebras

Lau

Zhang

2015

Trans. Amer. Math. Soc.

View full text Add to dashboard Cite

Motivated by a result of Ky Fan in 1965, we establish a characterization of a left amenable F-algebra (which includes the group algebra and the Fourier algebra of a locally compact group and quantum group algebras, or more generally the predual algebra of a Hopf von Neumann algebra) in terms of a finite dimensional invariant subspace property. This is done by first revealing a fixed point property for the semigroup of norm one positive linear functionals in the algebra. Our result answers an open question posted in Tokyo in 1993 by the first author (see [25, Problem 5]). We also show that the left amenability of an ideal in an F-algebra may determine the left amenability of the algebra. 1 2 A. T.-M. LAU AND Y. ZHANG invertible linear mappings that preserve the quadratic form J( x) = x 2 + y 2 + z 2 − c 2 t 2 , x = (x, y, z, t) ∈ R 4 where the constant c is the speed of light. Quantity J represents the space time interval. It is a well known fact that for any Lorentz transformation T there is a three dimensional subspace V of R 4 which is T -invariant and positive (in the sense that T ( x) = x and J( x) ≥ 0 for all x ∈ V ). L. S. Pontrjagin [43], I. S. Iovihdov [20], M. G. Krein [22, 21] and M. A. Naimark [40, 41] investigated infinite-dimension versions of the above invariant subspace property, and Naimark finally established the following theorem in 1963 [40].

show abstract

On ideals in the bidual of the Fourier algebra and related algebras

Abstract: Let G be a compact nonmetrizable topological group whose local weight b(G) has uncountable cofinality.

Cited by 5 publications

References 18 publications

Multiple disjointness and invariant measures on minimal distal flows

Multiple disjointness and invariant measures on minimal distal flows

Finite-dimensional left ideals in the duals of introverted spaces

Finite-dimensional invariant subspace property and amenability for a class of Banach algebras

Contact Info

Product

Resources

About