Coincidence of extendible vector-valued ideals with their minimal kernel
We provide coincidence results for vector-valued ideals of multilinear operators. More precisely, if A is an ideal of n-linear mappings we give conditions for which the equality A(E1,. . .,En;F)=Amin(E1,. . .,En;F) holds isometrically. As an application, we obtain in many cases that the monomials fo...
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_0022247X_v421_n2_p1743_Galicer |
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todo:paper_0022247X_v421_n2_p1743_Galicer2023-10-03T14:29:21Z Coincidence of extendible vector-valued ideals with their minimal kernel Galicer, D. Villafañe, R. Metric theory of tensor products Multilinear mappings Polynomial ideals Radon-Nikodým property We provide coincidence results for vector-valued ideals of multilinear operators. More precisely, if A is an ideal of n-linear mappings we give conditions for which the equality A(E1,. . .,En;F)=Amin(E1,. . .,En;F) holds isometrically. As an application, we obtain in many cases that the monomials form a Schauder basis of the space A(E1,. . .,En;F). Several structural and geometric properties are also derived using this equality. We apply our results to the particular case where A is the classical ideal of extendible or Pietsch-integral multilinear operators. Similar statements are given for ideals of vector-valued homogeneous polynomials. © 2014 Elsevier Inc. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_0022247X_v421_n2_p1743_Galicer |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Metric theory of tensor products Multilinear mappings Polynomial ideals Radon-Nikodým property |
| spellingShingle |
Metric theory of tensor products Multilinear mappings Polynomial ideals Radon-Nikodým property Galicer, D. Villafañe, R. Coincidence of extendible vector-valued ideals with their minimal kernel |
| topic_facet |
Metric theory of tensor products Multilinear mappings Polynomial ideals Radon-Nikodým property |
| description |
We provide coincidence results for vector-valued ideals of multilinear operators. More precisely, if A is an ideal of n-linear mappings we give conditions for which the equality A(E1,. . .,En;F)=Amin(E1,. . .,En;F) holds isometrically. As an application, we obtain in many cases that the monomials form a Schauder basis of the space A(E1,. . .,En;F). Several structural and geometric properties are also derived using this equality. We apply our results to the particular case where A is the classical ideal of extendible or Pietsch-integral multilinear operators. Similar statements are given for ideals of vector-valued homogeneous polynomials. © 2014 Elsevier Inc. |
| format |
JOUR |
| author |
Galicer, D. Villafañe, R. |
| author_facet |
Galicer, D. Villafañe, R. |
| author_sort |
Galicer, D. |
| title |
Coincidence of extendible vector-valued ideals with their minimal kernel |
| title_short |
Coincidence of extendible vector-valued ideals with their minimal kernel |
| title_full |
Coincidence of extendible vector-valued ideals with their minimal kernel |
| title_fullStr |
Coincidence of extendible vector-valued ideals with their minimal kernel |
| title_full_unstemmed |
Coincidence of extendible vector-valued ideals with their minimal kernel |
| title_sort |
coincidence of extendible vector-valued ideals with their minimal kernel |
| url |
http://hdl.handle.net/20.500.12110/paper_0022247X_v421_n2_p1743_Galicer |
| work_keys_str_mv |
AT galicerd coincidenceofextendiblevectorvaluedidealswiththeirminimalkernel AT villafaner coincidenceofextendiblevectorvaluedidealswiththeirminimalkernel |
| _version_ |
1782025395463258112 |