Abstract
A nonnormable ℱ-space possessing an unconditional basis is not necessarily isomorphic to a generalized Köthe space.
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M. M. Dragilev, Bases in Köthe Spaces [in Russian], Rostov state university, Rostov-on-Don, 1983, 2003.
A. Dynin and B. Mitiagin, “Criterion for nuclearity in terms of approximative dimension,” Bull. Acad. Polon. Sci. Ser. Math., 8 (1960), no. 8, 535–540.
G. Köthe and O. Toeplitz, “Lineare Räume mit unendlich vielen Koordinaten und Ringe unendlicher Matrizen,” J. Reine Angew. Math., 171 (1934), 251–270.
E. R. Lorch, “Bicontinuous linear transformation in certain vector spaces,” Bull. Amer. Math. Soc., 45 (1939), no. 2, 564–569.
I. M. Gelfand, “A remark on the paper by N. K. Bari “Biorthogonal systems and bases in Hilbert space,” Uchen. Zap. MGU. Ser. Matem., 4 (1951), no. 148, 224–225.
A. Pełczyński, “Projections in certain Banach spaces,” Studia Math., 19 (1960), 209–228.
J. Lindenstrauss and M. Zippin, “Banach spaces with a unique unconditional basis,” J. Funct. Anal., 3 (1969), 115–125.
A. Pełczyński and J. Singer, “On non-equivalent bases and conditional bases in Banach spaces,” Studia Math., 25 (1964), no. 1, 5–25.
W. Wojtinski, “On bases in certain countably Hilbert spaces,” Bull. Acad. Polon. Sci. Ser. Math., 14 (1966), no. 12, 681–684.
J. Lindenstrauss and A. Pełczyński, “Absolutely summing operators in Lp spaces and their applications,” Studia Math., 29 (1968), 275–326.
V. P. Zaharyuta, “Quasiequivalence of bases in finte centers of Hilbert scaes,” Dokl. Akad. Nauk SSSR [Soviet Math. Dokl.], 180 (1968), no. 4, 786–788.
B. S. Mityagin, “Equivalence of bases in Hilbert scales,” Studia Math., 37 (1971), no. 2, 111–137.
V. P. Kondakov, Some Problems of Isomorphism and Bases in Locally Convex Spaces, Cand. Sci. (Phys.-Math.) Dissertation, Rostov State Unversity, Rostov-on-Don, 1972.
N. J. Kalton, “On absolute bases,” Math. An., 200 (1973), 209–225.
M. Zippin, “On perfectly homogeneous bases in Banach spaces,” Israel J. Math., 4 (1966), 265–272.
V. P. Kondakov, Geometry of Nonnormable Spaces, Rostov State Unversity, Rostov-on-Don, 1983.
J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces I, II, Springer-Verlag, Berlin, Heidelberg, New York, 1977, 1979.
V. M. Tikhomirov, “On n-dimensional widths of some function classes,” Dokl. Akad. Nauk SSSR [Soviet Math. Dokl.], 130 (1960), no. 4, 734–737.
V. M. Tikhomirov, “Set widths in function spaces and the theory of best approximations,” Uspekhi Mat. Nauk [Russian Math. Surveys], 15 (1960), no. 3, 81–120.
V. M. Tikhomirov, Some Problems of Approximation Theory [in Russian], Moscow State University, Moscow, 1976.
P. A. Chalov, “Bernstein widths of sets in coordinate Orlicz spaces,” in: Teor. Funkts., Funkts. Analiz i Ikh Prilozh., No. 35, Vyshchya Shkola, Kharkov, 1981, pp. 119–123.
B. S. Mityagin, “Approximate dimension and bases in nuclear spaces,” Uspekhi Mat. Nauk [Russian Math. Surveys], 16 (1961), no. 4, 63–132.
G. Metafune and V. B. Moscatelli, “On the space ℓp+Iq>p∓q,” Math. Nachr., 147 (1990), 7–12.
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Translated from Matematicheskie Zametki, vol. 80, no. 1, 2006, pp. 29–32.
Original Russian Text Copyright © 2006 by M. M. Dragilev, P. A. Chalov.
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Dragilev, M.M., Chalov, P.A. Fréchet spaces with unconditional base. Math Notes 80, 27–30 (2006). https://doi.org/10.1007/s11006-006-0104-9
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DOI: https://doi.org/10.1007/s11006-006-0104-9