Commutative neutrix convolution products of functions
The commutative neutrix convolution product of the functions and is evaluated for and all . Further commutative neutrix convolution products are then deduced.
The commutative neutrix convolution product of the functions and is evaluated for and all . Further commutative neutrix convolution products are then deduced.
There has been a considerable search for radical, amenable Banach algebras. Noncommutative examples were finally found by Volker Runde [R]; here we present the first commutative examples. Centrally placed within the construction, the reader may be pleased to notice a reprise of the undergraduate argument that shows that a normed space with totally bounded unit ball is finite-dimensional; we use the same idea (approximate the norm 1 vector x within distance η by a “good” vector ; then approximate...
In this paper we define the notions of semicommutativity and semicommutativity modulo a linear subspace. We prove some results regarding the semicommutativity or semicommutativity modulo a linear subspace of a sequentially complete m-convex algebra. We show how such results can be applied in order to obtain commutativity criterions for locally m-convex algebras.
Let be an inclusion of factors with finite Jones index. Then as a vector space. Here denotes the vector space spanned by the commutators of the form where .
We prove the Schatten-Lorentz ideal criteria for commutators of multiplications and projections based on the Calderón reproducing formula and the decomposition theorem for the space of symbols corresponding to commutators in the Schatten ideal.
The set of commutators in a Banach *-algebra A, with continuous involution, is examined. Applications are made to the case where A = B(ℓ₂), the algebra of all bounded linear operators on ℓ₂.
It is proved that the set Q of quasinilpotent elements in a Banach algebra is an ideal, i.e. equal to the Jacobson radical, if (and only if) the condition [Q,Q] ⊆ Q (or a similar condition concerning anticommutators) holds. In fact, if the inner derivation defined by a quasinilpotent element p maps Q into itself then p ∈ Rad A. Higher commutator conditions of quasinilpotents are also studied. It is shown that if a Banach algebra satisfies such a condition, then every quasinilpotent element has some...
A classical theorem of Coifman, Rochberg, and Weiss on commutators of singular integrals is extended to the case of generalized Lp spaces with variable exponent.
Let be the fractional maximal function. The commutator generated by and a suitable function is defined by . Denote by the set of all measurable functions such that and by the set of all such that the Hardy-Littlewood maximal function is bounded on . In this paper, the authors give some characterizations of for which is bounded from into , when , and with .
Let T be a bounded linear operator on with 1 ≤ q < ∞ and 1 < p < ∞. Then T is a commutator if and only if for all non-zero λ ∈ ℂ, the operator T - λI is not X-strictly singular.