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Bulletin of the American Mathematical Society

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Book Review

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MathSciNet review: 1567387
Full text of review: PDF   This review is available free of charge.
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?)

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  • M. DeWilde, Closed graph theorems and webbed spaces, London-San Francisco-Melbourne, 1978. N. Dunford and J. T. Schwartz, Linear operators. I, Interscience, New York, 1958.
  • 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
  • Alexandre Grothendieck, Produits tensoriels topologiques et espaces nucléaires, Mem. Amer. Math. Soc. 16 (1955), Chapter 1: 196 pp.; Chapter 2: 140 (French). MR 75539
  • A. Grothendieck, Résumé de la théorie métrique des produits tensoriels topologiques, Bol. Soc. Mat. São Paulo 8 (1953), 1–79 (French). MR 94682
  • P. Halmos, Measure theory, Princeton Univ. Press, Princeton, N. J., 1961. J. Horváth, Review of Grothendieck's "Topological vector spaces", Bull. Amer. Math. Soc. 84 (1976), 515-521.
  • John Horváth, Topological vector spaces and distributions. Vol. I, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1966. MR 0205028
  • J. L. Kelley and Isaac Namioka, Linear topological spaces, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J., 1963. 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. MR 0166578
  • Gottfried Köthe, Topological vector spaces. I, Die Grundlehren der mathematischen Wissenschaften, Band 159, Springer-Verlag New York Inc., New York, 1969. Translated from the German by D. J. H. Garling. MR 0248498
  • J. Lindenstrauss and A. Pełczyński, Absolutely summing operators in $L_{p}$-spaces and their applications, Studia Math. 29 (1968), 275–326. MR 231188, DOI
  • 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
  • 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
  • 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
  • W. Rudin, Real and complex analysis, McGraw-Hill, New York and London, 1970. W. Ruess, Halbnorm-Dualitat und induktive Limestopologien in die Theorie lokalkonvexer Räume, Habil. schr. Univ. Bonn, 1976. H. H. Schaefer, Topological vector spaces, Macmillan, New York-Heidelberg-Berlin, 1971.
  • Albert Wilansky, Functional analysis, Blaisdell Publishing Co. Ginn and Co. New York-Toronto-London, 1964. MR 0170186
  • M. Zippin, The separable extension problem, Israel J. Math. 26 (1977), no. 3-4, 372–387. MR 442649, DOI

Review Information:

Reviewer: James R. Retherford
Journal: Bull. Amer. Math. Soc. 7 (1982), 612-615