The operators on Lp = Lp[0, 1], 1 ≤ p < ∞, which are not commutators are those of the form λI + S where λ , 0 and S belongs to the largest ideal in L(Lp). The proof involves new structural results for operators on Lp which are of independent interest.

in this paper, we verify the solvability of free product of finite cyclic groups with topological methods. we use cayley graphs and everitt methods to construct suitable 2-complexes corresponding to the presentations of groups and their commutator subgroups. in particular, using these methods, we prove that the commutator subgroup of $mathbb{z}_{m}*mathbb{z}_{n}$ is free of rank $(m-1)(n-1)$ fo...

We clarify the relationship between the linear commutator and the ordinary commutator by showing that in any variety satisfying a nontrivial idempotent Mal’cev condition the linear commutator is definable in terms of the centralizer relation. We derive from this that abelian algebras are quasi–affine in such varieties. We refine this by showing that if A is an abelian algebra and V(A) satisfies...

The question considered is the effect on the canonical commutation rules of mass renormalization in quantum etectrodynamics. This is investigated by considering the quantum Langevin equation for a charged quantum oscillator interacting with the radiation field via dipole interaction. Explicit expressions for the commutator are obtained for finite cutoff frequency as well as the large-cutoff lim...

We show that the universal central extensions of the little projective group of any Moufang polygon is precisely the Steinberg group obtained from its defining commutator relations, provided the defining structure is not too small. As an application, we get that also the universal central extensions of the little projective group of any 2-spherical Moufang twin building is precisely the Steinbe...