Some applications of an inequality in locally convex spaces

Some applications of an inequality in locally convex spaces
HTML articles powered by AMS MathViewer

Trans. Amer. Math. Soc. 137 (1969), 115-123

DOI: https://doi.org/10.1090/S0002-9947-1969-0239391-0

PDF | Request permission

References

Maynard G. Arsove, The Paley-Wiener theorem in metric linear spaces, Pacific J. Math. 10 (1960), 365–379. MR 125429, DOI 10.2140/pjm.1960.10.365
C. Bessaga and A. Pełczyński, On bases and unconditional convergence of series in Banach spaces, Studia Math. 17 (1958), 151–164. MR 115069, DOI 10.4064/sm-17-2-151-164
Mahlon M. Day, Normed linear spaces, Reihe: Reelle Funktionen, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1958. MR 0094675
J. Dixmier, Les fonctionnelles linéaires sur l’ensemble des opérateurs bornés d’un espace de Hilbert, Ann. of Math. (2) 51 (1950), 387–408 (French). MR 33445, DOI 10.2307/1969331
M. Krein, D. Milman, and M. Rutman, A note on basis in Banach space, Comm. Inst. Sci. Math. Méc. Univ. Kharkoff [Zapiski Inst. Mat. Mech.] (4) 16 (1940), 106–110 (Russian, with English summary). MR 0004709
Charles W. McArthur, A convergence criterion with applications to series in locally convex spaces, Duke Math. J. 34 (1967), 193–199. MR 206672
James R. Retherford, Basic sequences and the Paley-Wiener criterion, Pacific J. Math. 14 (1964), 1019–1027. MR 170195, DOI 10.2140/pjm.1964.14.1019
Helmut H. Schaefer, Topological vector spaces, The Macmillan Company, New York; Collier Macmillan Ltd., London, 1966. MR 0193469
I. Singer, Basic sequences and reflexivity of Banach spaces, Studia Math. 21 (1961/62), 351–369. MR 146635, DOI 10.4064/sm-21-3-351-369

Some stability properties of bases

5

L. J. Weill, Stability of bases in complete barrelled spaces, Proc. Amer. Math. Soc. 18 (1967), 1045–1050. MR 217553, DOI 10.1090/S0002-9939-1967-0217553-X