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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(e) ISSN 0273-0979(p)

     

Book Review

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Book Information

Author(s): A. Grothendieck
Title: Topological vector spaces
Additional book information: Gordon and Breach, New York, London, Paris, 1973, x + 245 pp., $19.50. (Translated by Orlando Chaljub)


References:

1.
J. Batt, P. Dierolf and J. Voigt, Summable sequences and topological properties of m (to appear).
2.
S. R. Caradus, W. E. Pfaffenberger and B. Yood, Calkin algebras and algebras of operators on Banach spaces, Lecture Notes in Pure and Appl. Math., vol. 9, Dekker, New York, 1974. MR 415345
3.
M. De Wilde, Réseaux dans les espaces linéaires à semi-normes, Mém. Soc. Roy. Sci. Liège Coll. in-8° (5) 18 (1969), no. 2, 144 pp. MR 44 #3102. MR 285885
4.
M. De Wilde, Various types of barrelledness and increasing sequences of balanced and convex sets in locally convex spaces, Lecture Notes in Math., vol. 331, Springer-Verlag, Berlin, Heidelberg, New York, 1973, pp. 211-217. MR 482031
5.
M. De Wilde and C. Houet, On increasing sequences of absolutely convex sets in locally convex spaces, Math. Ann. 192 (1971), 257-261. MR 44 #5746. MR 288549
6.
M. Dostal, Some recent results on topological vector spaces, Lecture Notes in Math., vol. 384, Springer-Verlag, Berlin, Heidelberg, New York, 1974, pp. 21-97. MR 397437
7.
A. Douady, Parties compacte d'un espace de fonctions continues à support compact, C. R. Acad. Sci. Paris 257 (1963), 2788-2791. MR 27 #6121. MR 156190
8.
V. Eberhardt, Durch Graphensätze definierte lokalkonvexe Räume, Thesis, München, 1972.
9.
V. Eberhardt, Über einen Graphensatz für Abbildungen mit normiertem Zielraum, Manuscripta Math. 12 (1974), 47-65. MR 49 #1056. MR 336280
10.
V. Eberhardt, Einige Vererbbarkeitseigenschaften von B- und B, Math. Ann. 215 (1975), 1-11. MR 370119
11.
V. Eberhardt and W. Roelcke, Über einen Graphensatz für lineare Abbildungen mit metrisierbarem Zielraum, Manuscripta Math. 13 (1974), 53-68. MR 355517
12.
B. Fuchssteiner, Sandwich theorems and lattice semigroups, J. Functional Analysis 16 (1974), 1-14. MR 49 #10619. MR 345889
13.
G. B. Giráldez Tiebo, Teoremas de gráfico cerrado, nucleo cerrado y aplicación abierta, Thesis, Madrid, 1974.
14.
A. Grothendieck, Critères de compacité dans les espaces fonctionnels généraux, Amer. J. Math. 74 (1952), 168-186. MR 13, 857. MR 47313
15.
A. Grothendieck, Sur les applications linéaires failblement compactes d'espaces du type C(K), Canad. J. Math. 5 (1953), 129-173. MR 15, 438. MR 58866
16.
A. Grothendieck, Sur les espaces (F) et (DF), Summa Brasil. Math. 3 (1954), 57-123. MR 17, 765. MR 75542
17.
A. Grothendieck, Produits tensoriels topologiques et espaces nucléaries, Mem. Amer. Math. Soc. No. 16 (1955). MR 17, 763. MR 75539
18.
C. Harvey, On domination estimates and global existence, J. Math. Mech. 16 (1967), 675-702. MR 35 #5750. MR 214903
19.
J. Horváth, Quelques résultats de M. H. Powell sur le théorème du graphe fermé, Publ. Dép. Math. (Lyon) 10 (1973), 65-77. MR 51 # 1330. MR 365077
20.
T. Husain, Two new classes of locally convex spaces, Math. Ann. 166 (1966), 289-299. MR 35 #3406. MR 212535
21.
H. Jarchow, Nuclear locally convex spaces, Lecture notes, no. 13, University of Maryland, 1976. MR 461080
22.
P. Jimenez Guerra, Thesis, Madrid, 1974.
23.
G. Köthe, General linear transformations of locally convex spaces, Math. Ann. 159 (1965), 309-328. MR 33 #573. MR 192347
24.
M. Levin and S. Saxon, Every countable-codimensional subspace of a barrelled space is barrelled, Proc. Amer. Math. Soc. 29 (1971), 91-96. MR 43 #6691. MR 280972
25.
A. Marquina and P. Pérez Carreras, On quasibarrelled spaces, Manuscripta Math. 12 (1974), 387-398. MR 412760
26.
A. Marquina and P. Pérez Carreras, Other results in PB-barrelled spaces, Proc. Sympos. Functional Analysis, Istanbul, Silivri, 1973, pp. 115-116. MR 420190
27.
D. J. Randtke, Characterization of precompact maps, Schwartz spaces and nuclear spaces, Trans. Amer. Math. Soc. 165 (1972), 87-101. MR 46 #4139. MR 305009
28.
W. Robertson, On the closed graph theorem and spaces with webs, Proc. London Math. Soc. (3) 24 (1972), 692-738. MR 46 #5979. MR 306857
29.
W. Robertson, Sur le théorème du graphe fermé, Bull. Soc. Math. France Suppl. Mém. 31/32 (1972), 343-350. MR 385508
30.
S. A. Saxon, Nuclear and product spaces, Baire-like spaces, and the strongest locally convex topology, Math. Ann. 197 (1972), 87-106. MR 46 #4140. MR 305010
31.
S. A. Saxon, Some normed barrelled spaces which are not Baire, Math. Ann. 209 (1974), 153-160. MR 352925
32.
S. A. Saxon and A. R. Todd, A property of locally convex Baire spaces, Math. Ann. 206 (1973), 23-34. MR 48 #6865. MR 328523
33.
L. Scheller, Fortsetzungen additiver Funktionen auf Halbgruppen zwischen sub- und superadditiven Funktionalen, Thesis, Frankfurt am Main, 1973.
34.
L. Schwartz, Homomorphismes et applications complètement continues, C. R. Acad. Sci. Paris 236 (1953), 2472-2473. MR 15, 233. MR 57457
35.
F. Trèves, Locally convex spaces and linear partial differential equations Die Grundlehren der math. Wissenschaften, Band 146, Springer-Verlag, New York, 1967. MR 36 #6986. MR 223939
36.
F. Trèves, Applications of distributions to PDE theory, Amer. Math. Monthly 77 (1970), 241-248. MR 40 #6035. MR 252818
37.
M. Valdívia, A hereditary property in locally convex spaces, Ann. Inst. Fourier (Grenoble) 21 (1972), fasc. 2, 1-2. MR 48 #11967. MR 333642
38.
M. Valdívia, Absolutely convex sets in barrelled spaces, Ann. Inst. Fourier (Grenoble) 21 (1972), fasc. 2, 3-13. MR 48 #11968. MR 333643
39.
M. Valdívia, On final topologies, J. Reine Angew. Math. 251 (1971), 193-199. MR 45 #4108. MR 295040
40.
M. Valdívia, A class of bornological barrelled spaces which are not ultrabornological, Math. Ann. 194 (1971), 43-51. MR 47 #2307. MR 313753
41.
M. Valdívia, Some examples on quasi-barrelled spaces, Ann. Inst. Fourier (Grenoble) 22 (1972), fasc. 2, 21-26. MR 49 # 1053. MR 336277
42.
M. Valdívia, On nonbornological barrelled spaces, Ann. Inst. Fourier (Grenoble) 22 (1972), fasc. 2, 27-30. MR 49 # 1050. MR 336274


Additional Information:

Reviewer(s):
John Horváth

Review Information:
Journal: Bull. Amer. Math. Soc. 82 (1976), 515-521.
DOI: 10.1090/S0002-9904-1976-14076-1
PII: S 0002-9904(1976)14076-1




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