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• # Artykuł - szczegóły

## Studia Mathematica

2011 | 202 | 1 | 81-104

## M-ideals of homogeneous polynomials

EN

### Abstrakty

EN
We study the problem of whether $𝓟_{w}(ⁿE)$, 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 $𝓟_{w}(ⁿE)$ is an M-ideal in 𝓟(ⁿE), then $𝓟_{w}(ⁿE)$ coincides with $𝓟_{w0}(ⁿE)$ (n-homogeneous polynomials that are weakly continuous on bounded sets at 0). We introduce a polynomial version of property (M) and derive that if $𝓟_{w}(ⁿE) = 𝓟_{w0}(ⁿE)$ and 𝒦(E) is an M-ideal in 𝓛(E), then $𝓟_{w}(ⁿE)$ is an M-ideal in 𝓟(ⁿE). We also show that if $𝓟_{w}(ⁿE)$ 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.

81-104

wydano
2011

### Twórcy

autor
• Departamento de Matemática, Universidad de San Andrés, Vito Dumas 284, (B1644BID) Victoria, Buenos Aires, Argentina
• CONICET