Kernel theorems and nuclearity in idempotent mathematics. An algebraic   approach
  In the framework of idempotent mathematics, analogs of the classical kernel theorems of L. Schwartz and A. Grothendieck are studied. Idempotent versions of nuclear spaces (in the sense of A. Grothendieck) are discussed. The so-called algebraic approach is used. This means that the basic concepts and results (including those of "topological" nature) are simulated in purely algebraic terms. 
G.L. Litvinov and G.B. Shpiz