Commutator Lifting Inequalities and Interpolation

Commutators in Real Interpolation with Quasi-power Parameters

The basic higher order commutator theorem is formulated for the real interpolation methods associated with the quasi-power parameters, that is, the function spaces on which Hardy inequalities are valid. This theorem unifies and extends various results given by Cwikel, Jawerth, Milman, Rochberg, and others, and incorporates some results of Kalton to the context of commutator estimates for the re...

Entropy and Multivariable Interpolation

We define a new notion of entropy for operators on Fock spaces and positive definite multi-Toeplitz kernels on free semigroups. This is studied in connection with factorization theorems for (multi-Toeplitz, multi-analytic, etc.) operators on Fock spaces. These results lead to entropy inequalities and entropy formulas for positive definite multi-Toeplitz kernels on free semigroups (resp. multi-T...

Lifting Representations of Z - Groups

Let K be the kernel of an epimorphism G→ Z, where G is a finitely presented group. If K has infinitely many subgroups of index 2, 3 or 4, then it has uncountably many. Moreover, if K is the commutator subgroup of a classical knot group G, then any homomorphism from K onto the symmetric group S2 (resp. Z3) lifts to a homomorphism onto S3 (resp. alternating group A4).

Lifted flow cover inequalities for mixed 0-1 integer programs

We investigate strong inequalities for mixed 0-1 integer programs derived from flow cover inequalities. Flow cover inequalities are usually not facet defining and need to be lifted to obtain stronger inequalities. However, because of the sequential nature of the standard lifting techniques and the complexity of the optimization problems that have to be solved to obtain lifting coefficients, lif...

AUni¢ed Theoryof Commutator Estimates fora Class of Interpolation Methods