Embedding c 0 in bvca ( Σ , X )

Juan Carlos Ferrando; L. M. Sánchez Ruiz

Czechoslovak Mathematical Journal (2007)

  • Volume: 57, Issue: 2, page 679-688
  • ISSN: 0011-4642

Abstract

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If ( Ω , Σ ) is a measurable space and X a Banach space, we provide sufficient conditions on Σ and X in order to guarantee that b v c a ( Σ , X ) , the Banach space of all X -valued countably additive measures of bounded variation equipped with the variation norm, contains a copy of c 0 if and only if X does.

How to cite

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Ferrando, Juan Carlos, and Ruiz, L. M. Sánchez. "Embedding $c_0$ in ${\rm bvca}(\Sigma ,X)$." Czechoslovak Mathematical Journal 57.2 (2007): 679-688. <http://eudml.org/doc/31154>.

@article{Ferrando2007,
abstract = {If $(\Omega ,\Sigma ) $ is a measurable space and $X$ a Banach space, we provide sufficient conditions on $\Sigma $ and $X$ in order to guarantee that $\mathop \{\mathrm \{b\}vca\}( \Sigma ,X) $, the Banach space of all $X$-valued countably additive measures of bounded variation equipped with the variation norm, contains a copy of $c_\{0\}$ if and only if $X$ does.},
author = {Ferrando, Juan Carlos, Ruiz, L. M. Sánchez},
journal = {Czechoslovak Mathematical Journal},
keywords = {countably additive vector measure of bounded variation; Pettis integrable function space; copy of $c_\{0\}$; copy of $\ell _\{\infty \}$; Pettis integrable function space; copy of  ; copy of  },
language = {eng},
number = {2},
pages = {679-688},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Embedding $c_0$ in $\{\rm bvca\}(\Sigma ,X)$},
url = {http://eudml.org/doc/31154},
volume = {57},
year = {2007},
}

TY - JOUR
AU - Ferrando, Juan Carlos
AU - Ruiz, L. M. Sánchez
TI - Embedding $c_0$ in ${\rm bvca}(\Sigma ,X)$
JO - Czechoslovak Mathematical Journal
PY - 2007
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 57
IS - 2
SP - 679
EP - 688
AB - If $(\Omega ,\Sigma ) $ is a measurable space and $X$ a Banach space, we provide sufficient conditions on $\Sigma $ and $X$ in order to guarantee that $\mathop {\mathrm {b}vca}( \Sigma ,X) $, the Banach space of all $X$-valued countably additive measures of bounded variation equipped with the variation norm, contains a copy of $c_{0}$ if and only if $X$ does.
LA - eng
KW - countably additive vector measure of bounded variation; Pettis integrable function space; copy of $c_{0}$; copy of $\ell _{\infty }$; Pettis integrable function space; copy of  ; copy of 
UR - http://eudml.org/doc/31154
ER -

References

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  1. An averaging result for c 0 -sequences, Bull. Soc. Math. Belg., Sér. B 30 (1978), 83–87. (1978) Zbl0417.46019MR0549653
  2. Banach Spaces of Vector-Valued Functions. Lecture Notes in Mathematics Vol.  1676, Springer-Verlag, Berlin, 1997. (1997) MR1489231
  3. Sequences and Series in Banach Spaces, Graduate Texts in Mathematics, 92, Springer-Verlag, New York-Heidelberg-Berlin, 1984. (1984) MR0737004
  4. Vector Measures. Mathematical Surveys, No  15, Am. Math. Soc., Providence, 1977. (1977) MR0453964
  5. 10.1090/S0002-9939-1990-1012927-4, Proc. Am. Math. Soc. 109 (1990), 747–752. (1990) MR1012927DOI10.1090/S0002-9939-1990-1012927-4
  6. When does ( Σ , X ) contain a copy of  , Math. Scand. 74 (1994), 271–274. (1994) MR1298368
  7. Introduction to Banach Space, Matfyzpress, Prague, 1996. (1996) 
  8. Real and Abstract Analysis. Graduate Texts in Mathematics  25, Springer-Verlag, New York-Heidelberg-Berlin, 1975. (1975) MR0367121
  9. The weak Radon-Nikodým property in Banach spaces, Stud. Math. 64 (1979), 151–173. (1979) Zbl0405.46015MR0537118
  10. 10.1090/conm/052/840704, Contemp. Math. 52 (1986), 131–135. (1986) DOI10.1090/conm/052/840704
  11. Quand l’espace des mesures a variation bornée est-it faiblement sequentiellement complet, Proc. Am. Math. Soc. 90 (1984), 285–288. (French) (1984) MR0727251

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