Let f be a multiplier for the Drury-Arveson space H n of the unit ball, and let ζ1, ..., ζn denote the coordinate functions. We show that for each 1 ≤ i ≤ n, the commutator [M∗ f ,Mζi ] belongs to the Schatten class Cp, p > 2n. This leads to a localization result for multipliers.

The singular values of XY − Y X are the objects under investigation. Here, X and Y are square matrices with complex entries, and one of them has rank one. Hence, there are at most two non-trivial numbers among the commutator’s singular values, and the pairs of interest can be depicted in the plane. The emphasis will lie on the unexpectedly intriguing case in which both matrices are of rank one ...

In the context of devising geometrical integrators that retain qualitative features of the underlying solution, we present a family of numerical methods (the method of iterated commutators, [5, 13]) to integrate ordinary di erential equations that evolve on matrix Lie groups. The schemes apply to the problem of nding a numerical approximation to the solution of Y 0 = A(t;Y )Y; Y (0) = Y0; where...

For countably generated ideals, J , of B(H), geometric stability is necessary for the canonical spectral characterization of sums of (J , B(H))–commutators to hold. This answers a question raised by Dykema, Figiel, Weiss and Wodzicki. There are some ideals, J , having quasi–nilpotent elements that are not sums of (J , B(H))–commutators. Also, every trace on every geometrically stable ideal is a...

Relationship is clariied between the notions of linear extension of algebraic theories, and central extension, in the sense of commutator calculus, of their models. Varieties of algebras turn out to be nilpotent Maltsev precisely when their theories may be obtained as results of iterated linear extensions by bifunctors from the so called abelian theories. The latter theories are described; they...

We show that b ∈ BMO( n) if and only if the commutator [b, Iα] of the multiplication operator by b and the fractional integral operator Iα is bounded from generalized Morrey spaces Lp,φ( n) to Lq,φ q/p ( n), where φ is non-decreasing, and 1 < p < ∞, 0 < α < n and 1/q = 1/p− α/n.

The non-commutative tori provide probably the most accessible interesting examples of non-commutative differentiable manifolds. We can identify an ordinary n-torus rn with its algebra, C(rn), of continuous complex-valued functions under pointwise multiplication. But C(rn) is the universal C*-algebra generated by n commuting unitary operators. By definition, [15, 16, 50], a non-commutative n-tor...

Let G be a group and G′ its commutator subgroup. Denote by c G the minimal number such that every element ofG′ can be expressed as a product of at most c G commutators. A group G is called a c-group if c G is finite. For any positive integer n, denote by cn the class of groups with commutator length, c G n. Let Fn,t 〈x1, . . . , xn〉 andMn,t 〈x1, . . . , xn〉 be, respectively, the free nilpotent ...

In this paper, the (H ~b , L p) and (HK̇ q,~b , K̇ q ) type boundedness for the multilinear commutator associated with the Littlewood-paley operator are obtained.

Let Φ̃ be a root system of type F4, and let G be a group generated by non-trivial subgroups Ar, r ∈ Φ̃, satisfying some generalized Steinberg relations, which are also satisfied by root subgroups corresponding to a Moufang octagon. These relations can be considered as a generalization of the element-wise commutator relations in Chevalley groups. The Steinberg presentation specifies the groups sat...