A polynomial Hutton theorem with applications

作者：Botelho Geraldo^*; Polac Leticia

来源：Journal of Mathematical Analysis and Applications, 2014, 415(1): 294-301.

DOI：10.1016/j.jmaa.2014.01.056

• Banach spaces
• Finite rank operators
• Finite rank polynomials
• Approximation property
• Quasi-approximation property

Extending a classical linear result due to Hutton to a nonlinear setting, we prove that a continuous homogeneous polynomial between Banach spaces can be approximated by finite rank polynomials if and only if its adjoint can be approximated by finite rank linear operators. Among other consequences, we apply this result to generalize a classical result due to Aron and Schottenloher about the approximation property on spaces of polynomials and a recent result due to Caliskan and Rueda about the quasi-approximation property on projective symmetric tensor products.

• 出版日期2014-7-1