Complete boundedness of heat semigroups on the von Neumann algebra of hyperbolic groups

Mei, Tao

doi:10.1090/tran/6825

Cited by 10 publications

(11 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For example we may take Γ to be a nonabelian free group or a hyperbolic Coxeter group. The following Bochner-Riesz means are studied in [MdlS17]: for a fixed δ > 1 we take…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

“…We refer to [GdlH90, Gro87] for a complete description of hyperbolic groups. We merely remind that all hyperbolic groups are weakly amenable and the completely bounded radial Fourier multipliers have been characterized in [Oza08,MdlS17]. In particular, we denote by | | the usual word length function on a hyperbolic group Γ, then the Fourier multipliers…”

mentioning

confidence: 99%

“…defines a family of completely bounded maps on V N (Γ) with sup N B δ N cb < ∞ as soon as δ > 1 (see [MdlS17,Example 3.4…”

mentioning

confidence: 99%

See 2 more Smart Citations

Pointwise convergence of noncommutative Fourier series

Hong,

Wang,

Wang

2019

Preprint

View full text Add to dashboard Cite

This paper is devoted to the study of convergence of Fourier series for nonabelian groups and quantum groups. It is well-known that a number of approximation properties of groups can be interpreted as some summation methods and mean convergence of associated noncommutative Fourier series. Based on this framework, this work studies the refined counterpart of pointwise convergence of these Fourier series. We establish a general criterion of maximal inequalities for approximative identities of noncommutative Fourier multipliers. As a result we prove that for any countable discrete amenable group, there exists a sequence of finitely supported positive definite functions tending to 1 pointwise, so that the associated Fourier multipliers on noncommutative Lp-spaces satisfy the pointwise convergence for all 1 < p < ∞. In a similar fashion, we also obtain results for a large subclass of groups (as well as discrete quantum groups) with the Haagerup property and weak amenability. We also consider the analogues of Fejér means and Bochner-Riesz means in the noncommutative setting. Our results in particular apply to the almost everywhere convergence of Fourier series of Lp-functions on non-abelian compact groups. On the other hand, we obtain as a byproduct the dimension free bounds of noncommutative Hardy-Littlewood maximal inequalities associated with convex bodies. As an ingredient, our proof also provides a refined version of Junge-Le Merdy-Xu's square function estimates Hp(M) ≃ L • p (M) when p → 1.

show abstract

“…For example we may take Γ to be a nonabelian free group or a hyperbolic Coxeter group. The following Bochner-Riesz means are studied in [MdlS17]: for a fixed δ > 1 we take…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

mentioning

confidence: 99%

See 1 more Smart Citation

Pointwise convergence of noncommutative Fourier series

Hong,

Wang,

Wang

2019

Preprint

View full text Add to dashboard Cite

show abstract

“…Remark. Corollary 4 (i) was proved in [28] for L : λ g → ϕ(g)λ g with ϕ a symmetric conditionally negative function on G.…”

Section: Examplesmentioning

confidence: 96%

H∞-calculus for semigroup generators on BMO

Ferguson

Mei

Simanek

2019

Advances in Mathematics

Self Cite

View full text Add to dashboard Cite

We prove that the negative generator L of a semigroup of positive contractions on L ∞ has bounded H ∞ (Sη)-calculus on the associated Poisson semigroup-BMO space for any angle η > π/2, provided L satisfies Bakry-Emery's Γ 2 ≥ 0 criterion. Our arguments only rely on the properties of the underlying semigroup and works well in the noncommutative setting.A key ingredient of our argument is a type of quasi monotone properties for the subordinated semigroup Tt,α = e −tL α , 0 < α < 1, that is proved in the first part of this article.

show abstract

“…where k 0 and m 0 are defined as in (10), and satisfy k 0 Now observe that this expression corresponds to N telescoping series. Indeed, fixing j 1 , ..., j N −1 and defining…”

Section: Multi-radial Multipliers On Products Of Treesmentioning

confidence: 99%

Radial Schur multipliers on some generalisations of trees

Vergara¹

2019

Studia Math.

View full text Add to dashboard Cite

We give a characterisation of radial Schur multipliers on finite products of trees. The equivalent condition is that a certain generalised Hankel matrix involving the discrete derivatives of the radial function is a trace class operator. This extends Haagerup, Steenstrup and Szwarc's result for trees. The same condition can be expressed in terms of Besov spaces on the torus. We also prove a similar result for products of hyperbolic graphs and provide a sufficient condition for a function to define a radial Schur multiplier on a finite dimensional CAT(0) cube complex.

show abstract

Complete boundedness of heat semigroups on the von Neumann algebra of hyperbolic groups

Cited by 10 publications

References 23 publications

Pointwise convergence of noncommutative Fourier series

Pointwise convergence of noncommutative Fourier series

H∞-calculus for semigroup generators on BMO

Radial Schur multipliers on some generalisations of trees

Contact Info

Product

Resources

About