Additive commutators of operators belonging to two{sided ideals of B(H) are studied. J){commutators is characterized and found to equal IJ ; B(H)]. It is shown that three commutators are enough in I; B(H)], and that four are enough in I; J ]. Finally, some results about single commutators are proved, for example that every element of the Schatten class C p is a single (C p ; B(H)){commutator if...

Two measures of how near an arbitrary function between groups is to being a homomorphism are considered. These have properties similar to conjugates and commutators. The authors show that there is a rich theory based on these structures, and that this theory can be used to unify disparate approaches such as group cohomology and the transfer and to prove theorems. The proof of the Schur-Zassenha...

Electromagnetic mass shifts, equal-time commutators (ETC), and their relation are analyzed, using the Jost-Lehmann representation for the forvrard Compton amplitude, The divergences in 6m are determined by Lorentz scal@rs associated with the ETC (when these exist). These results are illustrated by models with currents bilinear and linear in canonical fields. Existence of the ETC implies that th...

We study the group of interval exchange transformations and obtain several characterizations of its commutator group. In particular, it turns out that the commutator group is generated by elements of order 2.

The concept of topological gyrogroups is a generalization group. In this work, ones prove that gyrogroup G metrizable iff has an {\omega}{\omega}-base and Frechet-Urysohn. Moreover, in gyrogroups, every (countably, sequentially) compact subset being strictly (strongly) Frechet-Urysohn having are all weakly three-space properties with H closed L-subgyrogroup