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Additional resources for Advanced Courses of Mathematical Analysis 2: Proceedings of the 2nd International School Granada, Spain 20 - 24 September 2004
The nuclear maps are always compact and integral, and the composition of two integral maps is nuclear. , with a quotient map from an L1-space onto E ) be integral. The right semi-integral operators are precisely the familiar absolutely summing operators, generalized and studied in the 1960’s by Mityagin, Pelczynski and Pietsch, among others, to 24 the important class of absolutely p-summing operators (1 5 p < m). 3. III. T h e kernel theorem and nuclear spaces. , the continuous bilinear maps on D x came from a “distributional kernel”, that is, a distribution in two variables K ( x ,y) E D’(W” x Rm) such that for cp E D(Rn) and 1c, E D(Rm), a), T(cp)(G)= (cp(x)lC,(y),K ( x ,Y ) ) = (cp €3 $7 K) that could be written formally as J K ( x ,y ) c p ( z ) $ ~ ( yd)x d y .
Math. 38, 4 (2001), 389-408. 5. A. Defant and K. Floret, Tensor norms and Operator Ideals. North Holland, , Amsterdam, 1993. 6. J. Diestel, A survey of results related t o the Dunford-Pettis property. Proc. of the Conference on Integration, Topology and Geometry in Linear Spaces,. Contemp. Math. 2 (1980), 15-60. 7. J. Diestel, H. Jarchow and A. Tongue, Absolutely Summing Operators. Cambridge Univ. Press, 1995. 8. G1 A. Grothendieck, Produits tensoriels topologiques et espaces nucle'aires. Mem. Amer.
Sci. Paris 233 (1951)’ 839-841. (5) Sur une notion de produit tensoriel topologique d’espaces wectoriels topologiques, et une classe remarquable d’espaces wectoriels like d cette notion. C . R. cad. ci. Paris 233 (1951), 1556-1558. 35 (6) Critkres de compacite' duns les espacies fonctionnels ge'ne'raux. Amer. J. of Math. 74 (1952), 168-186. (7) Sur les applications line'aires faiblement compactes d'espaces du type C(K). Canadian J. Math. 5 (1953), 129-173. (8) Sur les espaces de solutions d'une classe ge'ne'rale d'e'quations aux de'rive'es partielles.