M-Structures in vector-valued polynomial spaces
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(...
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todo:paper_09446532_v19_n3_p685_Dimant2023-10-03T15:49:16Z M-Structures in vector-valued polynomial spaces Dimant, V. Lassalle, S. Homogeneous polynomials M-ideals Weakly continuous on bounded sets polynomials 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. Fil:Dimant, V. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Lassalle, S. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_09446532_v19_n3_p685_Dimant |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Homogeneous polynomials M-ideals Weakly continuous on bounded sets polynomials |
| spellingShingle |
Homogeneous polynomials M-ideals Weakly continuous on bounded sets polynomials Dimant, V. Lassalle, S. M-Structures in vector-valued polynomial spaces |
| topic_facet |
Homogeneous polynomials M-ideals Weakly continuous on bounded sets polynomials |
| description |
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. |
| format |
JOUR |
| author |
Dimant, V. Lassalle, S. |
| author_facet |
Dimant, V. Lassalle, S. |
| author_sort |
Dimant, V. |
| title |
M-Structures in vector-valued polynomial spaces |
| title_short |
M-Structures in vector-valued polynomial spaces |
| title_full |
M-Structures in vector-valued polynomial spaces |
| title_fullStr |
M-Structures in vector-valued polynomial spaces |
| title_full_unstemmed |
M-Structures in vector-valued polynomial spaces |
| title_sort |
m-structures in vector-valued polynomial spaces |
| url |
http://hdl.handle.net/20.500.12110/paper_09446532_v19_n3_p685_Dimant |
| work_keys_str_mv |
AT dimantv mstructuresinvectorvaluedpolynomialspaces AT lassalles mstructuresinvectorvaluedpolynomialspaces |
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1782030804061257728 |