Multilinear operators on C ( K , X ) spaces

Ignacio Villanueva

Czechoslovak Mathematical Journal (2004)

  • Volume: 54, Issue: 1, page 31-54
  • ISSN: 0011-4642

Abstract

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Given Banach spaces  X , Y and a compact Hausdorff space  K , we use polymeasures to give necessary conditions for a multilinear operator from C ( K , X ) into  Y to be completely continuous (resp.  unconditionally converging). We deduce necessary and sufficient conditions for  X to have the Schur property (resp.  to contain no copy of  c 0 ), and for  K to be scattered. This extends results concerning linear operators.

How to cite

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Villanueva, Ignacio. "Multilinear operators on $C(K,X)$ spaces." Czechoslovak Mathematical Journal 54.1 (2004): 31-54. <http://eudml.org/doc/32440>.

@article{Villanueva2004,
abstract = {Given Banach spaces  $X$, $Y$ and a compact Hausdorff space  $K$, we use polymeasures to give necessary conditions for a multilinear operator from $C(K,X)$ into  $Y$ to be completely continuous (resp.  unconditionally converging). We deduce necessary and sufficient conditions for  $X$ to have the Schur property (resp.  to contain no copy of  $c_0$), and for  $K$ to be scattered. This extends results concerning linear operators.},
author = {Villanueva, Ignacio},
journal = {Czechoslovak Mathematical Journal},
keywords = {completely continuous; unconditionally converging; multilinear operators; $C(K,X)$ spaces; completely continuous operator; unconditionally converging operator; multilinear operator; spaces},
language = {eng},
number = {1},
pages = {31-54},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Multilinear operators on $C(K,X)$ spaces},
url = {http://eudml.org/doc/32440},
volume = {54},
year = {2004},
}

TY - JOUR
AU - Villanueva, Ignacio
TI - Multilinear operators on $C(K,X)$ spaces
JO - Czechoslovak Mathematical Journal
PY - 2004
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 54
IS - 1
SP - 31
EP - 54
AB - Given Banach spaces  $X$, $Y$ and a compact Hausdorff space  $K$, we use polymeasures to give necessary conditions for a multilinear operator from $C(K,X)$ into  $Y$ to be completely continuous (resp.  unconditionally converging). We deduce necessary and sufficient conditions for  $X$ to have the Schur property (resp.  to contain no copy of  $c_0$), and for  $K$ to be scattered. This extends results concerning linear operators.
LA - eng
KW - completely continuous; unconditionally converging; multilinear operators; $C(K,X)$ spaces; completely continuous operator; unconditionally converging operator; multilinear operator; spaces
UR - http://eudml.org/doc/32440
ER -

References

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