On multilinear mappings attaining their norms.

Maria Acosta

Studia Mathematica (1998)

  • Volume: 131, Issue: 2, page 155-165
  • ISSN: 0039-3223

Abstract

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We show, for any Banach spaces X and Y, the denseness of the set of bilinear forms on X × Y whose third Arens transpose attains its norm. We also prove the denseness of the set of norm attaining multilinear mappings in the class of multilinear mappings which are weakly continuous on bounded sets, under some additional assumptions on the Banach spaces, and give several examples of classical spaces satisfying these hypotheses.

How to cite

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Acosta, Maria. "On multilinear mappings attaining their norms.." Studia Mathematica 131.2 (1998): 155-165. <http://eudml.org/doc/216572>.

@article{Acosta1998,
abstract = {We show, for any Banach spaces X and Y, the denseness of the set of bilinear forms on X × Y whose third Arens transpose attains its norm. We also prove the denseness of the set of norm attaining multilinear mappings in the class of multilinear mappings which are weakly continuous on bounded sets, under some additional assumptions on the Banach spaces, and give several examples of classical spaces satisfying these hypotheses.},
author = {Acosta, Maria},
journal = {Studia Mathematica},
keywords = {norm-attaining; multilinear maps; bilinear continuous forms; product of Banach spaces; third Arens transpose; shrinking and monotone finite-dimensional decomposition},
language = {eng},
number = {2},
pages = {155-165},
title = {On multilinear mappings attaining their norms.},
url = {http://eudml.org/doc/216572},
volume = {131},
year = {1998},
}

TY - JOUR
AU - Acosta, Maria
TI - On multilinear mappings attaining their norms.
JO - Studia Mathematica
PY - 1998
VL - 131
IS - 2
SP - 155
EP - 165
AB - We show, for any Banach spaces X and Y, the denseness of the set of bilinear forms on X × Y whose third Arens transpose attains its norm. We also prove the denseness of the set of norm attaining multilinear mappings in the class of multilinear mappings which are weakly continuous on bounded sets, under some additional assumptions on the Banach spaces, and give several examples of classical spaces satisfying these hypotheses.
LA - eng
KW - norm-attaining; multilinear maps; bilinear continuous forms; product of Banach spaces; third Arens transpose; shrinking and monotone finite-dimensional decomposition
UR - http://eudml.org/doc/216572
ER -

References

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