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Abstract:

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.

Registro:

Documento: Artículo
Título:Symmetric multilinear forms on Hilbert spaces: Where do they attain their norm?
Autor:Carando, D.; Rodríguez, J.T.
Filiación:Departamento de Matemática – Pab I, Facultad de Cs. Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, 1428, Argentina
IMAS-CONICET, Argentina
Departamento de Matemática, NUCOMPA, Facultad de Cs. Exactas, Universidad Nacional del Centro de la Provincia de Buenos Aires, Tandil, 7000, Argentina
CONICET, Argentina
Palabras clave:Hilbert spaces; Multilinear forms; Norm attaining mappings; Hilbert spaces; Tensors; Multilinear forms; Real case; Symmetric tensors; Unit ball; Vector spaces
Año:2019
Volumen:563
Página de inicio:178
Página de fin:192
DOI: http://dx.doi.org/10.1016/j.laa.2018.10.023
Título revista:Linear Algebra and Its Applications
Título revista abreviado:Linear Algebra Its Appl
ISSN:00243795
CODEN:LAAPA
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00243795_v563_n_p178_Carando

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Citas:

---------- APA ----------
Carando, D. & Rodríguez, J.T. (2019) . Symmetric multilinear forms on Hilbert spaces: Where do they attain their norm?. Linear Algebra and Its Applications, 563, 178-192.
http://dx.doi.org/10.1016/j.laa.2018.10.023
---------- CHICAGO ----------
Carando, D., Rodríguez, J.T. "Symmetric multilinear forms on Hilbert spaces: Where do they attain their norm?" . Linear Algebra and Its Applications 563 (2019) : 178-192.
http://dx.doi.org/10.1016/j.laa.2018.10.023
---------- MLA ----------
Carando, D., Rodríguez, J.T. "Symmetric multilinear forms on Hilbert spaces: Where do they attain their norm?" . Linear Algebra and Its Applications, vol. 563, 2019, pp. 178-192.
http://dx.doi.org/10.1016/j.laa.2018.10.023
---------- VANCOUVER ----------
Carando, D., Rodríguez, J.T. Symmetric multilinear forms on Hilbert spaces: Where do they attain their norm?. Linear Algebra Its Appl. 2019;563:178-192.
http://dx.doi.org/10.1016/j.laa.2018.10.023