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The space lip $ \alpha $ and certain other spaces have duals with Cesàro bases


Author: Martin Buntinas
Journal: Proc. Amer. Math. Soc. 57 (1976), 233-237
MSC: Primary 46A45
DOI: https://doi.org/10.1090/S0002-9939-1976-0477673-7
MathSciNet review: 0477673
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Abstract: Banach sequence spaces whose duals are Banach sequence spaces with Toeplitz bases are characterized. For example, the duals of the lip $ \alpha $ spaces, for $ 0 < \alpha < 1$, are shown to have Cesàro bases. Also reflexive spaces with a Toeplitz basis are characterized and an equivalent form of the well-known theorem of F. and M. Riesz on the absolute continuity of measures is given.


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  • [1] M. Buntinas, On Toeplitz sections in sequence spaces, Proc. Cambridge Philos. Soc. 78 (1975), 451-460. MR 0410163 (53:13913)
  • [2] K. de Leeuw, Banach spaces of Lipschitz functions, Studia Math. 21 (1961/62), 55-66. MR 25 #4341. MR 0140927 (25:4341)
  • [3] G Goes, Complementary spaces of Fourier coefficients, convolutions, and generalized matrix transformations and operators between BK-spaces, J. Math. Mech. 10 (1961), 135-157. MR 23 #A2692. MR 0125389 (23:A2692)
  • [4] -, Summen von FK-Räumen. Funktionale Abschnittskonvergenz und Umkehrsätze, Tôhoku Math. J. (2) 26 (1975), 487-504. MR 0361720 (50:14165)
  • [5] V. Ja. Kozlov, On a generalization of the concept of a basis, Dokl. Akad. Nauk SSSR 73 (1950), 643-646. (Russian) MR 12, 110. MR 0036446 (12:110b)
  • [6] J. T. Marti, Introduction to the theory of bases, Springer-Verlag, New York, 1969. MR 0438075 (55:10994)
  • [7] H. Mirkil, Continuous translation of Hölder and Lipschitz functions, Canad. J. Math. 12 (1960), 674-685. MR 23 #A1993. MR 0124682 (23:A1993)
  • [8] Ja. M. Ceĭtlin, Reflexivity of spaces with a basis, Sibirsk. Mat. Ž. 8 (1967), 475-479 = Siberian Math. J. 8 (1967), 348-351. MR 35 #3403. MR 0212533 (35:3404)
  • [9] A. Wilansky, Functional analysis, Blaisdell, Waltham, Mass., 1964. MR 30 #425. MR 0170186 (30:425)
  • [10] K. Zeller, Allgemeine Eigenschaften von Limitierungsverfahren, Math. Z. 53 (1951), 463-487. MR 12, 604. MR 0039824 (12:604e)
  • [11] -, Approximation in Wirkfeldern von Summierungsverfahren, Arch. Math. 4 (1953), 425-431. MR 15, 618. MR 0060043 (15:618c)
  • [12] A. Zygmund, Trigonometric series. Vol. 1, 2nd rev. ed., reprint, Cambridge Univ. Press, New York, 1968. MR 38 #4882. MR 0236587 (38:4882)

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DOI: https://doi.org/10.1090/S0002-9939-1976-0477673-7
Article copyright: © Copyright 1976 American Mathematical Society

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