Artículo
M-ideals of homogeneous polynomials
Fecha de publicación:
02/2011
Editorial:
Polish Academy of Sciences. Institute of Mathematics
Revista:
Studia Mathematica
ISSN:
0039-3223
e-ISSN:
1730-6337
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Clasificación temática:
Resumen
We study the problem of whether Pw(nE), the space of n-homogeneous polynomials which are weakly continuous on bounded sets, is an M-ideal in the space P(nE) of continuous n-homogeneous polynomials. We obtain conditions that ensure this fact and present some examples. We prove that if Pw(nE) is an M-ideal in P(nE), then Pw(nE) coincides with Pwo(nE) (n-homogeneous polynomials that are weakly continuous on bounded sets at 0). We introduce a polynomial version of property (M) and derive that if P w(nE) = Pw0(nE) and κ(E) is an M-ideal in (E), then Pw(nE) is an Mideal in P( nE). We also show that if Pw(nE) is an M-ideal in P(nE), then the set of n-homogeneous polynomials whose Aron-Berner extension does not attain its norm is nowhere dense in P(nE). Finally, we discuss an analogous M-ideal problem for block diagonal polynomials.
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Citación
Dimant, Veronica Isabel; M-ideals of homogeneous polynomials; Polish Academy of Sciences. Institute of Mathematics; Studia Mathematica; 202; 1; 2-2011; 81-104
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