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.

A study was made pertaining to the variations in sensitivity to inhibitors that may be encountered in industrial deterioration problems. The results indicate that at least three types of variations are involved: first, the variation in sensitivity of different strains, secondly, the variation in sensitivity of an individual strain, and finally, the variation produced by the particular environme...

In a first course in functional analysis, a great deal of time is spent with Banach spaces, especially the interaction between such spaces and their dual spaces. Banach spaces are a special type of topological vector space, and there are important topological vector spaces which do not lie in the Banach category, such as the Schwartz spaces. The most fundamental theorem about Banach spaces is t...

In the title salt, C6H10N3O2 (+)·C7H7O3S(-), the imidazole ring makes a dihedral angle of 70.93 (12)° with the plane of the toluene ring. In the crystal, the ions are linked via N-H⋯O and weak C-H⋯O hydrogen bonds forming two-dimensional networks lying parallel to (001). These networks are linked via C-H⋯π inter-actions, forming a three-dimensional structure.