Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5774748 | Journal of Mathematical Analysis and Applications | 2017 | 18 Pages |
Abstract
This paper is motivated by a long-standing conjecture of Dinculeanu from 1967. Let X and Y be Banach spaces and let Ω be a compact Hausdorff space. Dinculeanu conjectured that there exist operators SâL(C(Ω),L(X,Y)) which are not associated to any UâL(C(Ω,X),Y). We study this existence problem systematically on three possible levels of generality: the classical case C(Ω,X) of continuous vector-valued functions, p-continuous vector-valued functions, and tensor products. On each level, we establish necessary and sufficient conditions for an L(X,Y)-valued operator to be associated to a Y-valued operator. Among others, we see that examples, proving Dinculeanu's conjecture, come out on the all three levels of generality.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Fernando Muñoz, Eve Oja, Cándido Piñeiro,