# On multilinear mappings attaining their norms.

Studia Mathematica (1998)

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

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topAcosta, 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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