Symmetric multilinear forms on Hilbert spaces: Where do they attain their norm?

We characterize the sets of norm one vectors x1,…,xk in a Hilbert space H such that there exists a k-linear symmetric form attaining its norm at (x1,…,xk). We prove that in the bilinear case, any two vectors satisfy this property. However, for k≥3 only collinear vectors satisfy this property in the...

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Autores principales: Carando, D., Rodríguez, J.T.
Formato: JOUR
Materias:
Hilbert spaces
Multilinear forms
Norm attaining mappings
Tensors
Real case
Symmetric tensors
Unit ball
Vector spaces
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00243795_v563_n_p178_Carando
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_00243795_v563_n_p178_Carando
record_format dspace
spelling todo:paper_00243795_v563_n_p178_Carando2023-10-03T14:34:50Z Symmetric multilinear forms on Hilbert spaces: Where do they attain their norm? Carando, D. Rodríguez, J.T. Hilbert spaces Multilinear forms Norm attaining mappings Hilbert spaces Tensors Multilinear forms Real case Symmetric tensors Unit ball Vector spaces We characterize the sets of norm one vectors x1,…,xk in a Hilbert space H such that there exists a k-linear symmetric form attaining its norm at (x1,…,xk). We prove that in the bilinear case, any two vectors satisfy this property. However, for k≥3 only collinear vectors satisfy this property in the complex case, while in the real case this is equivalent to x1,…,xk spanning a subspace of dimension at most 2. We use these results to obtain some applications to symmetric multilinear forms, symmetric tensor products and the exposed points of the unit ball of Ls(Hk). © 2018 Elsevier Inc. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00243795_v563_n_p178_Carando
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Hilbert spaces
Multilinear forms
Norm attaining mappings
Hilbert spaces
Tensors
Multilinear forms
Real case
Symmetric tensors
Unit ball
Vector spaces
spellingShingle Hilbert spaces
Multilinear forms
Norm attaining mappings
Hilbert spaces
Tensors
Multilinear forms
Real case
Symmetric tensors
Unit ball
Vector spaces
Carando, D.
Rodríguez, J.T.
Symmetric multilinear forms on Hilbert spaces: Where do they attain their norm?
topic_facet Hilbert spaces
Multilinear forms
Norm attaining mappings
Hilbert spaces
Tensors
Multilinear forms
Real case
Symmetric tensors
Unit ball
Vector spaces
description We characterize the sets of norm one vectors x1,…,xk in a Hilbert space H such that there exists a k-linear symmetric form attaining its norm at (x1,…,xk). We prove that in the bilinear case, any two vectors satisfy this property. However, for k≥3 only collinear vectors satisfy this property in the complex case, while in the real case this is equivalent to x1,…,xk spanning a subspace of dimension at most 2. We use these results to obtain some applications to symmetric multilinear forms, symmetric tensor products and the exposed points of the unit ball of Ls(Hk). © 2018 Elsevier Inc.
format JOUR
author Carando, D.
Rodríguez, J.T.
author_facet Carando, D.
Rodríguez, J.T.
author_sort Carando, D.
title Symmetric multilinear forms on Hilbert spaces: Where do they attain their norm?
title_short Symmetric multilinear forms on Hilbert spaces: Where do they attain their norm?
title_full Symmetric multilinear forms on Hilbert spaces: Where do they attain their norm?
title_fullStr Symmetric multilinear forms on Hilbert spaces: Where do they attain their norm?
title_full_unstemmed Symmetric multilinear forms on Hilbert spaces: Where do they attain their norm?
title_sort symmetric multilinear forms on hilbert spaces: where do they attain their norm?
url http://hdl.handle.net/20.500.12110/paper_00243795_v563_n_p178_Carando
work_keys_str_mv AT carandod symmetricmultilinearformsonhilbertspaceswheredotheyattaintheirnorm
AT rodriguezjt symmetricmultilinearformsonhilbertspaceswheredotheyattaintheirnorm
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