Extreme integral polynomials on a complex Banach space

• Autores: Seán Dineen
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 92, Nº 1, 2003, págs. 129-140
• Idioma: inglés
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• Resumen

  • We obtain upper and lower set-theoretic inclusion estimates for the set of extreme points of the unit balls of $\mathcal{P}_{I}({}^{n}\!E)$ and $\mathcal{P}_{N}({}^{n}\!E)$, the spaces of $n$-homogeneous integral and nuclear polynomials, respectively, on a complex Banach space $E$. For certain collections of Banach spaces we fully characterise these extreme points. Our results show a difference between the real and complex space cases.