Bulletin of the American Mathematical Society

MathSciNet review: 1567275
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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.

C. Bessaga and Ed Dubinsky, Nuclear Fréchet spaces without bases. III. Every nuclear Fréchet space not isomorphic to $\omega$ 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, DOI 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).

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 365080, DOI 10.4064/sm-52-3-203-207

4.

M. M. Dragilev, On regular bases in nuclear spaces, Amer. Math. Soc Transl. 93 (1970), 61-82.

Ed Dubinsky, Subspaces without bases in nuclear Fréchet spaces, J. Functional Analysis 26 (1977), no. 2, 121–130. MR 0458112, DOI 10.1016/0022-1236(77)90007-6

Ed Dubinsky, The structure of nuclear Fréchet spaces, Lecture Notes in Mathematics, vol. 720, Springer, Berlin, 1979. MR 537039

Ed Dubinsky and Boris Mitiagin, Quotient spaces without bases in nuclear Fréchet spaces, Canadian J. Math. 30 (1978), no. 6, 1296–1305. MR 511563, DOI 10.4153/CJM-1978-106-9

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 132376

Per Enflo, A counterexample to the approximation problem in Banach spaces, Acta Math. 130 (1973), 309–317. MR 402468, DOI 10.1007/BF02392270

Alexandre Grothendieck, Produits tensoriels topologiques et espaces nucléaires, Mem. Amer. Math. Soc. 16 (1955), Chapter 1: 196 pp.; Chapter 2: 140 (French). MR 75539

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.

B. S. Mitjagin, Approximate dimension and bases in nuclear spaces, Uspehi Mat. Nauk 16 (1961), no. 4 (100), 63–132 (Russian). MR 0152865

B. S. Mitjagin, Equivalence of bases in Hilbert scales, Studia Math. 37 (1970/71), 111–137 (Russian). MR 322470

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.

Albrecht Pietsch, Nukleare lokalkonvexe Räume, Schriftenreihe Inst. Math. Deutsch. Akad. Wiss. Berlin, Reihe A, Reine Mathematik, Heft 1, Akademie-Verlag, Berlin, 1965 (German). MR 0181888

Dietmar Vogt, Subspaces and quotient spaces of $(s)$, Functional analysis: surveys and recent results (Proc. Conf., Paderborn, 1976) North-Holland Math. Studies, Vol. 27; Notas de Mat., No. 63, North-Holland, Amsterdam, 1977, pp. 167–187. MR 0625306

V. P. Zahariuta, On the isomorphism of cartesian products of locally convex spaces, Studia Math. 46 (1973), 201–221. MR 330991, DOI 10.4064/sm-46-3-201-221

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

1.

C. Bessaga and Ed Dubinsky, Nuclear Fréchet spaces without bases, Arch. Math. 31 (1978), 597-604. MR 0531575

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.

L. Crone and W. B. Robinson, Every nuclear Fréchet space with a regular basis has the quasi-equivalence property, Studia Math. 52 (1975), 203-207. MR 365080

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 Anal. 26 (1977), 121-130. MR 458112

6.

Ed Dubinsky, The structure of nuclear Fréchet spaces, Lecture Notes in Math. vol 720, Springer-Verlag, Berlin and New York. MR 537039

7.

Ed Dubinsky and Boris Mityagin, Quotient spaces without bases in nuclear Fréchet spaces, Canad. J. Math. 30 (1978), 1296-1305. MR 511563

8.

A. S. Dynin and B. S. Mityagin, Criterion for nuclearity in terms of approximative dimension, Bull Acad. Polon. Sci. Sér Sci Math. Astronom. Phys. 8 (1960), 535-540. MR 132376

9.

P. Enflo, A counter example to the approximation problem in Banach spaces, Acta Math. 130 (1973), 309-317. MR 402468

10.

A. Grothendieck, Produits tensoriels topologiques et espaces nucleaires, Mem. Amer. Math. Soc. No. 16 (1955). MR 75539

11.

G. Henkin and B. S. Mityagin, Linear problems of complex analysis, Uspehi Mat Nauk. 26 (4) (1972), 95-152. (Russian) MR 287297

12.

T. Kōmura and Y. Kōmura, Ūber die einbettung der nuklearen Räume im (s), Math. Ann. 162 (1966), 284-288.

13.

B. S. Mityagin, Approximative dimension and bases in nuclear spaces, Uspehi Mat Nauk. 16 (4) (1961), 73-132. (Russian) MR 152865

14.

B. S. Mityagin, Equivalence of bases in Hilbert scales, Studia Math. 37 (1971), 111-137. (Russian) MR 322470

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.

A. Pietsch, Nukleare Lokalkonvexe Räume, Berlin, 1965. MR 181888

17.

D. Vogt, Subspaces and quotient spaces of (s), Functional Analysis, Surveys and Recent Results, (Proc. Conf., Padenborn, 1976), North-Holland, Amsterdam, 1977, pp. 167-187. MR 625306

18.

V. P. Zahariuta, On the isomorphism of Cartesian products of locally convex spaces, Studia Math 46 (1973), 201-221. MR 330991

19.

V. P. Zahariuta, Generalized Mityagin invariants and a continuum of pairwise nonisomorphic spaces of analytic functions, Funkcional Anal. i Priložen 11 (1977), 24-30. (Russian) MR 467268