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Bulletin of the American Mathematical Society

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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. III. Every nuclear Fréchet space not isomorphic to 𝜔 admits a subspace and a quotient space without a strong finite-dimensional decomposition, Arch. Math. (Basel) 31 (1978/79), no. 6, 597–604. MR 531575, https://doi.org/10.1007/BF01226497
  • 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. Lawrence Crone and William B. Robinson, Every nuclear Fréchet space with a regular basis has the quasi-equivalence property, Studia Math. 52 (1974/75), 203–207. MR 0365080
  • 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 Analysis 26 (1977), no. 2, 121–130. MR 0458112
  • 6. Ed Dubinsky, The structure of nuclear Fréchet spaces, Lecture Notes in Mathematics, vol. 720, Springer, Berlin, 1979. MR 537039
  • 7. Ed Dubinsky and Boris Mitiagin, Quotient spaces without bases in nuclear Fréchet spaces, Canad. J. Math. 30 (1978), no. 6, 1296–1305. MR 511563, https://doi.org/10.4153/CJM-1978-106-9
  • 8. A. Dynin and B. Mitiagin, Criterion for nuclearity in terms of approximative dimension, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 8 (1960), 535–540 (English, with Russian summary). MR 0132376
  • 9. Per Enflo, A counterexample to the approximation problem in Banach spaces, Acta Math. 130 (1973), 309–317. MR 0402468, https://doi.org/10.1007/BF02392270
  • 10. Alexandre Grothendieck, Produits tensoriels topologiques et espaces nucléaires, Mem. Amer. Math. Soc. No. 16 (1955), 140 (French). MR 0075539
  • 11. B. S. Mitjagin and G. M. Henkin, Linear problems of complex analysis, Uspehi Mat. Nauk 26 (1971), no. 4 (160), 93–152 (Russian). MR 0287297
  • 12. T. Kōmura and Y. Kōmura, Ūber die einbettung der nuklearen Räume im (s), Math. Ann. 162 (1966), 284-288.
  • 13. B. S. Mitjagin, Approximate dimension and bases in nuclear spaces, Uspehi Mat. Nauk 16 (1961), no. 4 (100), 63–132 (Russian). MR 0152865
  • 14. B. S. Mitjagin, Equivalence of bases in Hilbert scales, Studia Math. 37 (1970/71), 111–137 (Russian). MR 0322470
  • 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. Albrecht Pietsch, Nukleare lokalkonvexe Räume, Schriftenreihe der Institute Für Mathematik bei der Deutschen Akademie der Wissenschaften zu Berlin. Reihe A, Reine Mathematik, Heft 1, Akademie-Verlag, Berlin, 1965 (German). MR 0181888
  • 17. Dietmar Vogt, Subspaces and quotient spaces of (𝑠), Functional analysis: surveys and recent results (Proc. Conf., Paderborn, 1976) North-Holland, Amsterdam, 1977, pp. 167–187. North-Holland Math. Studies, Vol. 27; Notas de Mat., No. 63. MR 0625306
  • 18. V. P. Zahariuta, On the isomorphism of cartesian products of locally convex spaces, Studia Math. 46 (1973), 201–221. MR 0330991
  • 19. V. P. Zaharjuta, Generalized Mitjagin invariants and a continuum of mutually non-isomorphic spaces of analytic functions, Funkcional. Anal. i Priložen. 11 (1977), no. 3, 24–30, 96 (Russian). MR 0467268

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