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. We use the so-called algebraic approach, which means that the basic concepts and results (including those of “topological” nature) are simulated in purely algebraic terms. Bibliography: 33 titles. In dear memory of F. A. Berezin __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 331, 2006, pp. 60–83.