Noncommutative harmonic analysis on semigroups

Noncommutative Harmonic Analysis on Semigroup and Ultracontractivity

We extend some classical results of Cowling and Meda to the noncommutative setting. Let (Tt)t>0 be a symmetric contraction semigroup on a noncommutative space Lp(M), and let the functions φ and ψ be regularly related. We prove that the semigroup (Tt)t>0 is φ-ultracontractive, i.e. ‖Ttx‖∞ ≤ Cφ(t)‖x‖1 for all x ∈ L1(M) and t > 0 if and only if its infinitesimal generator L has the Sobolev embeddi...

Noncommutative Dynamics and E-semigroups

Noncommutative Disc Algebras for Semigroups

We study noncommutative disc algebras associated to the free product of discrete subsemigroups of R +. These algebras are associated to generalized Cuntz algebras, which are shown to be simple and purely innnite. The nonself-adjoint subalgebras determine the semigroup up to isomorphism. Moreover, we establish a dilation theorem for contractive representations of these semigroups which yields a ...

Noncommutative Wold Decompositions for Semigroups of Isometries

The structure of the isometric representations of unital discrete semi-groups with the left cancellation property and no divisors of the identity is studied. We obtain Wold decompositions and prove that the left regular representation of such semigroups is irreducible.

Markov Bases for Noncommutative Harmonic Analysis of Partially Ranked Data

Given the result v0 of a survey and a nested collection of summary statistics that could be used to describe that result, it is natural to ask which of these summary statistics best describe v0. In 1998 Diaconis and Sturmfels presented an approach for determining the conditional significance of a higher order statistic, after sampling a space conditioned on the value of a lower order statistic....