Book Review
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MathSciNet review:
1567387
Full text of review:
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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.
W. J. Davis, T. Figiel, W. B. Johnson, and A. Pełczyński, Factoring weakly compact operators, J. Functional Analysis 17 (1974), 311–327. MR 0355536, DOI 10.1016/0022-1236(74)90044-5
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.
A. Grothendieck, Topological vector spaces, Notes on Mathematics and its Applications, Gordon and Breach Science Publishers, New York-London-Paris, 1973. Translated from the French by Orlando Chaljub. 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
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.
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 10.4064/sm-29-3-275-326
Joram Lindenstrauss and Lior Tzafriri, Classical Banach spaces. I, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 92, Springer-Verlag, Berlin-New York, 1977. Sequence spaces. 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, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 66, Springer-Verlag, New York-Heidelberg, 1972. Translated from the second German edition by William H. Ruckle. MR 0350360
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.
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 10.1007/BF03007653
- 1.
- W. Davis, T. Figiel, W. Johnson, and A. Pełczyński, Factoring weakly compact operators, J. Funct Anal. 17 (1974), 311-327. MR 0355536
- 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, Gorden & Breach, New York-London-Paris, 1973. MR 372565
- 5.
- A. Grothendieck, Products tensoriels topologiques et espaces nucléaires, Mem. Amer. Math. Soc. No. 16 (1955). MR 75539
- 6.
- A. Grothendieck, Résumé de la théorie métrique des produits tensoriels topologiques, Bol. Soc. Mat. Sào. Paulo 8 (1953), 1-79. MR 94682
- 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.
- J. Horváth, Topological vector spaces and distributions. I, Addison-Wesley, Reading, Mass., 1966. MR 205028
- 10.
- J. L. Kelley and I. Namioka, Linear topological spaces, Van Nostrand, Princeton, N. J., 1963. MR 166578
- 11.
- G. Köthe, Topological vector spaces. I, Springer-Verlag, Berlin-Heidelberg-New York, 1969. MR 248498
- 12.
- J. Lindenstrauss and A. Pełczyński, Absolutely summing operators in L, Studia Math. 29 (1968), 275-326. MR 231188
- 13.
- J. Lindenstrauss and L. Tzafriri, Classical Banach spaces. I, Lecture Notes in Math., Vol. 338, Springer-Verlag, Berlin-Heidelberg-New Tork, 1977. MR 500056
- 14.
- A. Pietsch, Operator ideals, Amsterdam-Oxford-New York, 1980. MR 582655
- 15.
- A. Pietsch (translated by W. Ruckle), Nuclear locally convex spaces, Springer-Verlag, Berlin-Heidelberg-New York, 1972. MR 350360
- 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.
- A. Wilansky, Functional analysis, Blaisdell, Waltham, Mass., 1964. MR 170186
- 20.
- M. Zippin, The separable extension problem, Israel J. Math. 26 (1977), 372-387. MR 442649
Review Information:
Reviewer:
James R. Retherford
Journal:
Bull. Amer. Math. Soc.
7 (1982), 612-615
DOI:
https://doi.org/10.1090/S0273-0979-1982-15069-8
