Proceedings of the American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support My Subscriptions Help
ISSN 1088-6826(e) ISSN 0002-9939(p)

A note on sequences lying in the range of a vector measure valued in the bidual

Author(s): Begoña Marchena; Cándido Piñeiro
Journal: Proc. Amer. Math. Soc. 126 (1998), 3013-3017.
MSC (1991): Primary 46G10, 47B10
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract: Let be a Banach space. It is unknown if every subset of lying in the range of an $X^{**}$ -valued measure is actually contained in the range of an -valued measure. In this paper we solve this problem in the case when we consider only vector measures of bounded variation.

References:

[AD]: R. Anantharaman and J. Diestel, Sequences in the range of a vector measure, Annales Societatis Mathematicae Polonae, Serie I: Comm. Math. XXX (1991), 221-235. MR 92g:46049
[BD]: J. Bourgain and F. Delbaen, A class of special ${\mathcal{L}}_{\infty }$ -spaces, Acta Math. 145 (1980), 155-176. MR 82h:46023
[DU]: J. Diestel and J.J. Uhl, Jr, Vector measures, Math. Surveys 15, Amer. Math. Soc, Providence, R.I, 1977. MR 56:12216
[G]: J.C. García-Vázquez, Tensor products of vector measures and sequences in the range of a vector measure, Proc. Amer. Math. Soc. 124 (1996), 3459-3467. MR 97f:46030
[J]: H. Jarchow, Locally Convex Spaces, B.G. Teubner, Stuttgart, 1981. MR 83h:46008
[LR]: J. Lindenstrauss and H.P. Rosenthal, The ${\mathcal{L}}_{p}$ spaces, Israel J. Math. 7 (1969), 325-349. MR 42:5012
[MR]: J.S. Morrel and J.R.Retherford, P-Trivial Banach Spaces, Studia Math. XLIII(1) (1972), 1-25. MR 47:2321
[Pi1]: C.Piñeiro, Sequences in the range of a vector measure with bounded variation, Proc. Amer. Math. Soc. 123 (1995), 3329-3334. MR 96a:46033
[Pi2]: C. Piñeiro, On p-summable sequences in the range of a vector measure, Proc. Amer. Math. Soc. 125 (1997), 2073-2082. MR 97i:46082
[PR]: C. Piñeiro and L. Rodriguez-Piazza, Banach spaces in which every compact lies inside the range of a measure, Proc. Amer. Math. Soc. 114 (1992), 505-517. MR 92e:46038
[Ps]: G. Pisier, Factorization of linear operators and geometry of Banach spaces, CBMS, vol.60, Amer. Math. Soc., Providence, R.I., 1986. MR 88a:47020
[SR]: C.P. Steagall and J.R. Retherford, Fully nuclear and completely nuclear operators with applications to ${\mathcal{L}}_{1}$ and ${\mathcal{L}}_{\infty }$ -spaces, Transac. Amer. Math. Soc. 163 (1972), 457-491. MR 54:3368

	Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
\|