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Book Review

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Book Information:

Author: Yau-Chuen Wong
Title: Schwartz spaces, nuclear spaces and tensor products
Additional book information: Lecture Notes in Math., vol 726, Springer-Verlag, Berlin-Heidelberg-New York, 1979, viii + 418 pp., $19.50.

References [Enhancements On Off] (What's this?)

  • 1. C. Bessaga and Ed Dubinsky, Nuclear Fréchet spaces without bases, Arch. Math. 31 (1978), 597-604. MR 531575
  • 2. Manfred Bōrgens, Reinhold Meise and Dietmar Vogt, Functions holomorphes sur certains espaces échelonnés et λ-nuclearité, C. R. Acad. Sci. Paris (to appear).
  • 3. L. Crone and W. B. Robinson, Every nuclear Fréchet space with a regular basis has the quasi-equivalence property, Studia Math. 52 (1975), 203-207. MR 365080
  • 4. M. M. Dragilev, On regular bases in nuclear spaces, Amer. Math. Soc Transl. 93 (1970), 61-82.
  • 5. Ed Dubinsky, Subspaces without bases in nuclear Fréchet spaces, J. Functional Anal. 26 (1977), 121-130. MR 458112
  • 6. Ed Dubinsky, The structure of nuclear Fréchet spaces, Lecture Notes in Math. vol 720, Springer-Verlag, Berlin and New York. MR 537039
  • 7. Ed Dubinsky and Boris Mityagin, Quotient spaces without bases in nuclear Fréchet spaces, Canad. J. Math. 30 (1978), 1296-1305. MR 511563
  • 8. A. S. Dynin and B. S. Mityagin, Criterion for nuclearity in terms of approximative dimension, Bull Acad. Polon. Sci. Sér Sci Math. Astronom. Phys. 8 (1960), 535-540. MR 132376
  • 9. P. Enflo, A counter example to the approximation problem in Banach spaces, Acta Math. 130 (1973), 309-317. MR 402468
  • 10. A. Grothendieck, Produits tensoriels topologiques et espaces nucleaires, Mem. Amer. Math. Soc. No. 16 (1955). MR 75539
  • 11. G. Henkin and B. S. Mityagin, Linear problems of complex analysis, Uspehi Mat Nauk. 26 (4) (1972), 95-152. (Russian) MR 287297
  • 12. T. Kōmura and Y. Kōmura, Ūber die einbettung der nuklearen Räume im (s), Math. Ann. 162 (1966), 284-288.
  • 13. B. S. Mityagin, Approximative dimension and bases in nuclear spaces, Uspehi Mat Nauk. 16 (4) (1961), 73-132. (Russian) MR 152865
  • 14. B. S. Mityagin, Equivalence of bases in Hilbert scales, Studia Math. 37 (1971), 111-137. (Russian) MR 322470
  • 15. B. S. Mityagin and N. M. Zobin, Contre-exemple à l'existence d'une base dans un espace de Fréchet nucleaire, C. R. Acad. Sci. Paris Sér. A. 279 (1974), 255-256; 325-327.
  • 16. A. Pietsch, Nukleare Lokalkonvexe Räume, Berlin, 1965. MR 181888
  • 17. D. Vogt, Subspaces and quotient spaces of (s), Functional Analysis, Surveys and Recent Results, (Proc. Conf., Padenborn, 1976), North-Holland, Amsterdam, 1977, pp. 167-187. MR 625306
  • 18. V. P. Zahariuta, On the isomorphism of Cartesian products of locally convex spaces, Studia Math 46 (1973), 201-221. MR 330991
  • 19. V. P. Zahariuta, Generalized Mityagin invariants and a continuum of pairwise nonisomorphic spaces of analytic functions, Funkcional Anal. i Priložen 11 (1977), 24-30. (Russian) MR 467268

Review Information:

Reviewer: Ed Dubinsky
Journal: Bull. Amer. Math. Soc. 3 (1980), 762-766
DOI: https://doi.org/10.1090/S0273-0979-1980-14814-4
American Mathematical Society