Previous |  Up |  Next


Title: On Pettis integrability (English)
Author: Ferrando, J. C.
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 53
Issue: 4
Year: 2003
Pages: 1009-1015
Summary lang: English
Category: math
Summary: Assuming that $(\Omega , \Sigma , \mu )$ is a complete probability space and $X$ a Banach space, in this paper we investigate the problem of the $X$-inheritance of certain copies of $c_0$ or $\ell _{\infty }$ in the linear space of all [classes of] $X$-valued $\mu $-weakly measurable Pettis integrable functions equipped with the usual semivariation norm. (English)
Keyword: Pettis integrable function space
Keyword: copy of $c_0$
Keyword: copy of $\ell _{\infty }$
Keyword: countably additive vector measure
Keyword: WRNP
Keyword: CRP
MSC: 28B05
MSC: 46G10
idZBL: Zbl 1080.46515
idMR: MR2018846
Date available: 2009-09-24T11:08:42Z
Last updated: 2020-07-03
Stable URL:
Reference: [1] P.  Cembranos and J.  Mendoza: Banach Spaces of Vector-Valued Functions. Lecture Notes in Math. 1676.Springer, 1997. MR 1489231
Reference: [2] J.  Diestel: Sequences and Series in Banach Spaces. GTM 92.Springer Verlag. New York-Berlin-Heidelberg-Tokyo, 1984. MR 0737004
Reference: [3] J.  Diestel and J.  Uhl: Vector Measures. Math Surveys 15.Amer. Math. Soc. Providence, 1977. MR 0453964
Reference: [4] L.  Drewnowski: Copies of $\ell _{\infty }$ in an operator space.Math. Proc. Camb. Phil. Soc. 108 (1990), 523–526. MR 1068453, 10.1017/S0305004100069401
Reference: [5] L.  Drewnowski, M.  Florencio and P. J.  Paúl: The space of Pettis integrable functions is barrelled.Proc. Amer. Math. Soc. 114 (1992), 687–694. MR 1107271, 10.1090/S0002-9939-1992-1107271-2
Reference: [6] D.  van Dulst: Characterizations of Banach Spaces not containing $\ell _{1}$. CWI Tract.Amsterdam, 1989. MR 1002733
Reference: [7] J. C.  Ferrando: On sums of Pettis integrable random elements.Quaestiones Math. 25 (2002), 311–316. Zbl 1036.46010, MR 1931282, 10.2989/16073600209486018
Reference: [8] F. J.  Freniche: Embedding $c_0$ in the space of Pettis integrable functions.Quaestiones Math. 21 (1998), 261–267. Zbl 0963.46025, MR 1701785, 10.1080/16073606.1998.9632045
Reference: [9] E.  Hewitt and K.  Stromberg: Real and Abstract Analysis. GTM 25.Springer Verlag, 1965. MR 0367121
Reference: [10] K.  Musial: The weak Radon-Nikodým property in Banach spaces.Studia Math. 64 (1979), 151–173. Zbl 0405.46015, MR 0537118, 10.4064/sm-64-2-151-174


Files Size Format View
CzechMathJ_53-2003-4_18.pdf 320.8Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo