Random trilinear forms and the Schur multiplication of tensors.
Rank α operators on the space C(T,X)
For 0 ≤ α < 1, an operator U ∈ L(X,Y) is called a rank α operator if implies Uxₙ → Ux in norm. We give some results on rank α operators, including an interpolation result and a characterization of rank α operators U: C(T,X) → Y in terms of their representing measures.
Remarks on compact operators between interpolation spaces associated to polygons.
This note deals with interpolation methods defined by means of polygons. We show necessary and sufficient conditions for compactness of operators acting from a J-space into a K-space.
Representing non-weakly compact operators
For each S ∈ L(E) (with E a Banach space) the operator R(S) ∈ L(E**/E) is defined by R(S)(x** + E) = S**x** + E(x** ∈ E**). We study mapping properties of the correspondence S → R(S), which provides a representation R of the weak Calkin algebra L(E)/W(E) (here W(E) denotes the weakly compact operators on E). Our results display strongly varying behaviour of R. For instance, there are no non-zero compact operators in Im(R) in the case of and C(0,1), but R(L(E)/W(E)) identifies isometrically with...