Geodesic
Kernel theorems and nuclearity in idempotent mathematics. An algebraic approach
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part XIV, Tome 331 (2006), pp. 60-83

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In the framework of idempotent mathematics, some analogs for the well-known kernel theorems of L. Schwartz and A. Grothendieck are examined. Idempotent versions of nuclear spaces (in the sense of A. Grothendieck) are described. An algebraic approach is used, so topological concepts and results are simulated by means of algebraic tools. 
@article{ZNSL_2006_331_a5,
     author = {G. L. Litvinov and G. B. Shpiz},
     title = {Kernel theorems and nuclearity in idempotent mathematics. {An} algebraic approach},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {60--83},
     publisher = {mathdoc},
     volume = {331},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2006_331_a5/}
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G. L. Litvinov; G. B. Shpiz. Kernel theorems and nuclearity in idempotent mathematics. An algebraic approach. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part XIV, Tome 331 (2006), pp. 60-83. http://geodesic.mathdoc.fr/item/ZNSL_2006_331_a5/