Integral linear operator

An integral bilinear form is a bilinear functional that belongs to the continuous dual space of $X{\widehat {\otimes }}_{\epsilon }Y$, the injective tensor product of the locally convex Topological Vector Spaces (TVSs) X and Y.

See also

• Auxiliary normed spaces
• Final topology
• Injective tensor product
• Nuclear operators
• Nuclear spaces
• Projective tensor product
• Topological tensor product

References

• Diestel, Joe (2008). The metric theory of tensor products : Grothendieck's résumé revisited. Providence, R.I: American Mathematical Society. ISBN 0-8218-4440-7. OCLC 185095773. {{cite book}}: Invalid |ref=harv (help)
• Dubinsky, Ed (1979). The structure of nuclear Fréchet spaces. Berlin New York: Springer-Verlag. ISBN 3-540-09504-7. OCLC 5126156. {{cite book}}: Invalid |ref=harv (help)
• Grothendieck, Grothendieck (1966). Produits tensoriels topologiques et espaces nucléaires (in French). Providence: American Mathematical Society. ISBN 0-8218-1216-5. OCLC 1315788. {{cite book}}: Invalid |ref=harv (help)
• Husain, Taqdir (1978). Barrelledness in topological and ordered vector spaces. Berlin New York: Springer-Verlag. ISBN 3-540-09096-7. OCLC 4493665. {{cite book}}: Invalid |ref=harv (help)
• Khaleelulla, S. M. (1982). Counterexamples in topological vector spaces. Berlin New York: Springer-Verlag. ISBN 978-3-540-11565-6. OCLC 8588370. {{cite book}}: Invalid |ref=harv (help)
• Nlend, H (1977). Bornologies and functional analysis : introductory course on the theory of duality topology-bornology and its use in functional analysis. Amsterdam New York New York: North-Holland Pub. Co. Sole distributors for the U.S.A. and Canada, Elsevier-North Holland. ISBN 0-7204-0712-5. OCLC 2798822. {{cite book}}: Invalid |ref=harv (help)
• Nlend, H (1981). Nuclear and conuclear spaces : introductory courses on nuclear and conuclear spaces in the light of the duality. Amsterdam New York New York, N.Y: North-Holland Pub. Co. Sole distributors for the U.S.A. and Canada, Elsevier North-Holland. ISBN 0-444-86207-2. OCLC 7553061. {{cite book}}: Invalid |ref=harv (help)
• Pietsch, Albrecht (1972). Nuclear locally convex spaces. Berlin,New York: Springer-Verlag. ISBN 0-387-05644-0. OCLC 539541. {{cite book}}: Invalid |ref=harv (help)
• Robertson, A. P. (1973). Topological vector spaces. Cambridge England: University Press. ISBN 0-521-29882-2. OCLC 589250. {{cite book}}: Invalid |ref=harv (help)
• Ryan, Raymond (2002). Introduction to tensor products of Banach spaces. London New York: Springer. ISBN 1-85233-437-1. OCLC 48092184. {{cite book}}: Invalid |ref=harv (help)
• Schaefer, Helmut H. (1999). Topological Vector Spaces. GTM. Vol. 3. New York, NY: Springer New York Imprint Springer. ISBN 978-1-4612-7155-0. OCLC 840278135. {{cite book}}: Invalid |ref=harv (help)
• Treves, François (2006). Topological vector spaces, distributions and kernels. Mineola, N.Y: Dover Publications. ISBN 978-0-486-45352-1. OCLC 853623322. {{cite book}}: Invalid |ref=harv (help)
• Wong (1979). Schwartz spaces, nuclear spaces, and tensor products. Berlin New York: Springer-Verlag. ISBN 3-540-09513-6. OCLC 5126158. {{cite book}}: Invalid |ref=harv (help)

External links

• Nuclear space at ncatlab