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Abstract:

This paper is concerned with the study of M-structures in spaces of polynomials. More precisely, we discuss for E and F Banach spaces, whether the class of weakly continuous on bounded sets n-homogeneous polynomials, p w( nE, F), is an M-ideal in the space of continuous n-homogeneous polynomials p( nE,F). We show that there is some hope for this to happen only for a finite range of values of n. We establish sufficient conditions under which the problem has positive and negative answers and use the obtained results to study the particular cases when E = l pand F = l q or F is a Lorentz sequence space d(w,q). We extend to our setting the notion of property (M) introduced by Kalton which allows us to lift M-structures from the linear to the vector-valued polynomial context. Also, when p w( nE,F) is an M-ideal in p( nE, F) we prove a Bishop-Phelps type result for vector-valued polynomials and relate norm-attaining polynomials with farthest points and remotal sets. © Heldermann Verlag.

Registro:

Documento: Artículo
Título:M-Structures in vector-valued polynomial spaces
Autor:Dimant, V.; Lassalle, S.
Filiación:Departamento de Matemática, Universidad de San Andrés, Vito Dumas 284, B1644BID Victoria, Buenos Aires, Argentina
CONICET, Argentina
Departamento de Matemática - Pab I, Facultad de Cs. Exactas Y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina
Palabras clave:Homogeneous polynomials; M-ideals; Weakly continuous on bounded sets polynomials
Año:2012
Volumen:19
Número:3
Página de inicio:685
Página de fin:711
Título revista:Journal of Convex Analysis
Título revista abreviado:J. Convex Anal.
ISSN:09446532
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09446532_v19_n3_p685_Dimant

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Citas:

---------- APA ----------
Dimant, V. & Lassalle, S. (2012) . M-Structures in vector-valued polynomial spaces. Journal of Convex Analysis, 19(3), 685-711.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09446532_v19_n3_p685_Dimant [ ]
---------- CHICAGO ----------
Dimant, V., Lassalle, S. "M-Structures in vector-valued polynomial spaces" . Journal of Convex Analysis 19, no. 3 (2012) : 685-711.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09446532_v19_n3_p685_Dimant [ ]
---------- MLA ----------
Dimant, V., Lassalle, S. "M-Structures in vector-valued polynomial spaces" . Journal of Convex Analysis, vol. 19, no. 3, 2012, pp. 685-711.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09446532_v19_n3_p685_Dimant [ ]
---------- VANCOUVER ----------
Dimant, V., Lassalle, S. M-Structures in vector-valued polynomial spaces. J. Convex Anal. 2012;19(3):685-711.
Available from: https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09446532_v19_n3_p685_Dimant [ ]