# Norm attaining multilinear forms and polynomials on preduals of Lorentz sequence spaces

M. Jimenéz Sevilla; Rafael Payá

Studia Mathematica (1998)

- Volume: 127, Issue: 2, page 99-112
- ISSN: 0039-3223

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topJimenéz Sevilla, M., and Payá, Rafael. "Norm attaining multilinear forms and polynomials on preduals of Lorentz sequence spaces." Studia Mathematica 127.2 (1998): 99-112. <http://eudml.org/doc/216467>.

@article{JimenézSevilla1998,

abstract = {For each natural number N, we give an example of a Banach space X such that the set of norm attaining N-linear forms is dense in the space of all continuous N-linear forms on X, but there are continuous (N+1)-linear forms on X which cannot be approximated by norm attaining (N+1)-linear forms. Actually,X is the canonical predual of a suitable Lorentz sequence space. We also get the analogous result for homogeneous polynomials.},

author = {Jimenéz Sevilla, M., Payá, Rafael},

journal = {Studia Mathematica},

keywords = {norm attaining multilinear forms and polynomials; weakly continuous multilinear forms and polynomials; Lorentz sequence spaces; norm attaining multilinear forms; Lorentz sequence space},

language = {eng},

number = {2},

pages = {99-112},

title = {Norm attaining multilinear forms and polynomials on preduals of Lorentz sequence spaces},

url = {http://eudml.org/doc/216467},

volume = {127},

year = {1998},

}

TY - JOUR

AU - Jimenéz Sevilla, M.

AU - Payá, Rafael

TI - Norm attaining multilinear forms and polynomials on preduals of Lorentz sequence spaces

JO - Studia Mathematica

PY - 1998

VL - 127

IS - 2

SP - 99

EP - 112

AB - For each natural number N, we give an example of a Banach space X such that the set of norm attaining N-linear forms is dense in the space of all continuous N-linear forms on X, but there are continuous (N+1)-linear forms on X which cannot be approximated by norm attaining (N+1)-linear forms. Actually,X is the canonical predual of a suitable Lorentz sequence space. We also get the analogous result for homogeneous polynomials.

LA - eng

KW - norm attaining multilinear forms and polynomials; weakly continuous multilinear forms and polynomials; Lorentz sequence spaces; norm attaining multilinear forms; Lorentz sequence space

UR - http://eudml.org/doc/216467

ER -

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