On vector valued measure spaces of bounded Φ -variation containing copies of

María J. Rivera

Czechoslovak Mathematical Journal (2001)

  • Volume: 51, Issue: 1, page 67-72
  • ISSN: 0011-4642

Abstract

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Given a Young function Φ , we study the existence of copies of c 0 and in c a b v Φ ( μ , X ) and in c a b s v Φ ( μ , X ) , the countably additive, μ -continuous, and X -valued measure spaces of bounded Φ -variation and bounded Φ -semivariation, respectively.

How to cite

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Rivera, María J.. "On vector valued measure spaces of bounded $\Phi $-variation containing copies of $\ell _\infty $." Czechoslovak Mathematical Journal 51.1 (2001): 67-72. <http://eudml.org/doc/30615>.

@article{Rivera2001,
abstract = {Given a Young function $\Phi $, we study the existence of copies of $c_0$ and $\ell _\{\infty \}$ in $\mathop \{\mathrm \{c\}abv\}\nolimits _\{\Phi \} (\mu ,X)$ and in $\mathop \{\mathrm \{c\}absv\}\nolimits _\{\Phi \} (\mu ,X)$, the countably additive, $\mu $-continuous, and $X$-valued measure spaces of bounded $\Phi $-variation and bounded $\Phi $-semivariation, respectively.},
author = {Rivera, María J.},
journal = {Czechoslovak Mathematical Journal},
keywords = {Young function; copies of and ; measure spaces},
language = {eng},
number = {1},
pages = {67-72},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On vector valued measure spaces of bounded $\Phi $-variation containing copies of $\ell _\infty $},
url = {http://eudml.org/doc/30615},
volume = {51},
year = {2001},
}

TY - JOUR
AU - Rivera, María J.
TI - On vector valued measure spaces of bounded $\Phi $-variation containing copies of $\ell _\infty $
JO - Czechoslovak Mathematical Journal
PY - 2001
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 51
IS - 1
SP - 67
EP - 72
AB - Given a Young function $\Phi $, we study the existence of copies of $c_0$ and $\ell _{\infty }$ in $\mathop {\mathrm {c}abv}\nolimits _{\Phi } (\mu ,X)$ and in $\mathop {\mathrm {c}absv}\nolimits _{\Phi } (\mu ,X)$, the countably additive, $\mu $-continuous, and $X$-valued measure spaces of bounded $\Phi $-variation and bounded $\Phi $-semivariation, respectively.
LA - eng
KW - Young function; copies of and ; measure spaces
UR - http://eudml.org/doc/30615
ER -

References

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  1. 10.2307/1988879, Trans. Amer. Math. Soc. 16 (1915), 435–501. (1915) MR1501024DOI10.2307/1988879
  2. The problem of complementability for some spaces of vector measures of bounded variation with values in Banach spaces containing copies of c 0 , Studia Math. 104 (1993), 110–123. (1993) MR1211812
  3. On complemented copies of c 0 in L X p , 1 p < , Proc. Amer. Math. Soc. 104, 785–786. 
  4. 10.7146/math.scand.a-12555, Math. Scand. 77 (1995), 148–152. (1995) MR1365911DOI10.7146/math.scand.a-12555
  5. Copies of in L p ( μ ; X ) , Proc. Amer. Math. Soc. 109 (1990), 125–127. (1990) MR1012935
  6. Theory of Orlicz Spaces, Marcel Dekker Inc., 1991. (1991) MR1113700
  7. 10.4064/sm-37-1-13-36, Studia Math. 37 (1970), 13–16. (1970) MR0270122DOI10.4064/sm-37-1-13-36
  8. Orlicz spaces of finitely additive set functions, Studia Math. XXIX (1967), 19–58. (1967) Zbl0158.13703MR0226395

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