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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(online) ISSN 0273-0979(print)

Book Review

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Full text of review: PDF

Book Information

Author: H. Jarchow
Title: Locally convex spaces
Additional book information Teubner, Stuttgart, 1981, 14 + 534 pp., DM 98,--.

Author: Albert Wilansky
Title: Modern methods in topological vector spaces
Additional book information McGraw-Hill, 1979, xiii + 298 pp., $39.95.


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

  • 1. W. J. Davis, T. Figiel, W. B. Johnson, and A. Pełczyński, Factoring weakly compact operators, J. Functional Analysis 17 (1974), 311–327. MR 0355536 (50 #8010)
  • 2. M. DeWilde, Closed graph theorems and webbed spaces, London-San Francisco-Melbourne, 1978.
  • 3. N. Dunford and J. T. Schwartz, Linear operators. I, Interscience, New York, 1958.
  • 4. A. Grothendieck, Topological vector spaces, Gordon and Breach Science Publishers, New York-London-Paris, 1973. Translated from the French by Orlando Chaljub; Notes on Mathematics and its Applications. MR 0372565 (51 #8772)
  • 5. Alexandre Grothendieck, Produits tensoriels topologiques et espaces nucléaires, Mem. Amer. Math. Soc. 1955 (1955), no. 16, 140 (French). MR 0075539 (17,763c)
  • 6. A. Grothendieck, Résumé de la théorie métrique des produits tensoriels topologiques, Bol. Soc. Mat. São Paulo 8 (1953), 1–79 (French). MR 0094682 (20 #1194)
  • 7. P. Halmos, Measure theory, Princeton Univ. Press, Princeton, N. J., 1961.
  • 8. J. Horváth, Review of Grothendieck's "Topological vector spaces", Bull. Amer. Math. Soc. 84 (1976), 515-521.
  • 9. John Horváth, Topological vector spaces and distributions. Vol. I, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1966. MR 0205028 (34 #4863)
  • 10. J. L. Kelley and Isaac Namioka, Linear topological spaces, With the collaboration of W. F. Donoghue, Jr., Kenneth R. Lucas, B. J. Pettis, Ebbe Thue Poulsen, G. Baley Price, Wendy Robertson, W. R. Scott, Kennan T. Smith. The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J., 1963. MR 0166578 (29 #3851)
  • 11. Gottfried Köthe, Topological vector spaces. I, Translated from the German by D. J. H. Garling. Die Grundlehren der mathematischen Wissenschaften, Band 159, Springer-Verlag New York Inc., New York, 1969. MR 0248498 (40 #1750)
  • 12. J. Lindenstrauss and A. Pełczyński, Absolutely summing operators in 𝐿_{𝑝}-spaces and their applications, Studia Math. 29 (1968), 275–326. MR 0231188 (37 #6743)
  • 13. Joram Lindenstrauss and Lior Tzafriri, Classical Banach spaces. I, Springer-Verlag, Berlin-New York, 1977. Sequence spaces; Ergebnisse der Mathematik und ihrer Grenzgebiete, Vol. 92. MR 0500056 (58 #17766)
  • 14. Albrecht Pietsch, Operator ideals, North-Holland Mathematical Library, vol. 20, North-Holland Publishing Co., Amsterdam-New York, 1980. Translated from German by the author. MR 582655 (81j:47001)
  • 15. Albrecht Pietsch, Nuclear locally convex spaces, Springer-Verlag, New York-Heidelberg, 1972. Translated from the second German edition by William H. Ruckle; Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 66. MR 0350360 (50 #2853)
  • 16. W. Rudin, Real and complex analysis, McGraw-Hill, New York and London, 1970.
  • 17. W. Ruess, Halbnorm-Dualitat und induktive Limestopologien in die Theorie lokalkonvexer Räume, Habil. schr. Univ. Bonn, 1976.
  • 18. H. H. Schaefer, Topological vector spaces, Macmillan, New York-Heidelberg-Berlin, 1971.
  • 19. Albert Wilansky, Functional analysis, Blaisdell Publishing Co. Ginn and Co. New York-Toronto-London, 1964. MR 0170186 (30 #425)
  • 20. M. Zippin, The separable extension problem, Israel J. Math. 26 (1977), no. 3-4, 372–387. MR 0442649 (56 #1030)


Review Information

Reviewer: James R. Retherford
Journal: Bull. Amer. Math. Soc. 7 (1982), 612-615
DOI: http://dx.doi.org/10.1090/S0273-0979-1982-15069-8
PII: S 0273-0979(1982)15069-8