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

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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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Autor principal: Carando, D.
Otros Autores: Rodríguez, J.T
Formato: Capítulo de libro
Lenguaje:Inglés
Publicado: Elsevier Inc. 2019
Acceso en línea:Registro en Scopus
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100 1 |a Carando, D. 
245 1 0 |a Symmetric multilinear forms on Hilbert spaces: Where do they attain their norm? 
260 |b Elsevier Inc.  |c 2019 
270 1 0 |m Rodríguez, J.T.; Departamento de Matemática, NUCOMPA, Facultad de Cs. Exactas, Universidad Nacional del Centro de la Provincia de Buenos AiresArgentina; email: jtrodrig@dm.uba.ar 
506 |2 openaire  |e Política editorial 
504 |a Acosta, M., Denseness of norm attaining mappings (2006) Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Math. RACSAM, 100 (1-2), pp. 9-30 
504 |a Acosta, M., Aron, R., García, D., Maestre, M., The Bishop–Phelps–Bollobás theorem for operators (2008) J. Funct. Anal., 254 (11), pp. 2780-2799 
504 |a Aron, R., Choi, Y., Kim, S.K., Lee, H.J., Martín, M., The Bishop–Phelps–Bollobás version of Lindenstrauss properties A and B (2015) Trans. Amer. Math. Soc., 367 (9), pp. 6085-6101 
504 |a Banach, S., Uber homogene Polynome in (L2) (1938) Studia Math., 7, pp. 36-44 
504 |a Benítez, C., Sarantopoulos, Y., Characterization of real inner product spaces by means of symmetrical bilinear forms (1993) J. Math. Anal. Appl., 180 (1), pp. 207-220 
504 |a Bochnak, J., Siciak, J., Polynomials and multilinear mappings in topological vector-spaces (1970) Studia Math., 39, pp. 59-76 
504 |a Dantas, S., García, D., Kim, S., Lee, H.J., Maestre, M., On the Bishop–Phelps–Bollobás theorem for multilinear mappings (2017) Linear Algebra Appl., 532, pp. 406-431 
504 |a Dineen, S., Complex analysis on infinite-dimensional spaces (1999), Springer-Verlag London; Floret, K., Natural norms on symmetric tensor products of normed spaces (1997) Note Mat., 17, pp. 153-188 
504 |a Friedland, S., Lim, L., Nuclear norm of high-order tensors (2018) Math. Comp., 18, pp. 1255-1281 
504 |a Grecu, B., Geometry of homogeneous polynomials on two-dimensional real Hilbert spaces (2004) J. Math. Anal. Appl., 293 (2), pp. 578-588 
504 |a Grecu, B., Muñoz-Fernández, G., Seoane-Sepúlveda, J.B., The unit ball of the complex P(H3) (2009) Math. Z., 263 (4), pp. 775-785 
504 |a Kim, S., Lee, S.H., Exposed 2-homogeneous polynomials on Hilbert spaces (2003) Proc. Amer. Math. Soc., 131 (2), pp. 449-453 
504 |a Minc, H., Permanents (1978) Encyclopedia of Mathematics and its Applications, 6. , Addison-Wesley Publishing Co. Reading, Mass 
504 |a Muñoz, G., Sarantopoulos, Y., Tonge, A., Complexifications of real Banach spaces, polynomials and multilinear maps (1999) Studia Math., 134 (1), pp. 1-33 
504 |a Nie, J., Symmetric tensor nuclear norms (2017) SIAM J. Appl. Algebra Geometry, 1 (1), pp. 599-625 
504 |a Pappas, A., Sarantopoulos, Y., Tonge, A., Norm attaining polynomials (2007) Bull. Lond. Math. Soc., 39 (2), pp. 255-264 
504 |a Rivlin, T., The Chebyshev Polynomials (1974) Pure and Applied Mathematics, , Wiley-Interscience [John Wiley & Sons] New York 
520 3 |a 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.  |l eng 
536 |a Detalles de la financiación: PIP 11220130100329CO 
536 |a Detalles de la financiación: UBACyT, 20020130100474, PICT 2015-2299 
536 |a Detalles de la financiación: This project was supported in part by CONICET PIP 11220130100329CO , ANPCyT PICT 2015-2299 and UBACyT 20020130100474 . 
593 |a Departamento de Matemática – Pab I, Facultad de Cs. Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, 1428, Argentina 
593 |a IMAS-CONICET, Argentina 
593 |a Departamento de Matemática, NUCOMPA, Facultad de Cs. Exactas, Universidad Nacional del Centro de la Provincia de Buenos Aires, Tandil, 7000, Argentina 
593 |a CONICET, Argentina 
690 1 0 |a HILBERT SPACES 
690 1 0 |a MULTILINEAR FORMS 
690 1 0 |a NORM ATTAINING MAPPINGS 
690 1 0 |a HILBERT SPACES 
690 1 0 |a TENSORS 
690 1 0 |a MULTILINEAR FORMS 
690 1 0 |a REAL CASE 
690 1 0 |a SYMMETRIC TENSORS 
690 1 0 |a UNIT BALL 
690 1 0 |a VECTOR SPACES 
700 1 |a Rodríguez, J.T. 
773 0 |d Elsevier Inc., 2019  |g v. 563  |h pp. 178-192  |p Linear Algebra Its Appl  |x 00243795  |w (AR-BaUEN)CENRE-248  |t Linear Algebra and Its Applications 
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