Locally compact semi-algebras generated by a commuting operator family.
Lucid operators on Banach spaces
l(Φ,φ) operators and (Φ,φ)-spaces.
A new class of linear and bounded operators is introduced. This class is more general than the classes of operators from [4], [5] and [8]. Using this class lΦ,φ we also introduce a class of locally convex spaces which is more general than the classes of the nuclear spaces [2], [3] and φ-nuclear spaces [6]. For this class of operators similar properties are established to those of the well known classes lp, lφ, lΦ and also the stability of the tensor product is proved. The stability of the tensor...