Extremal Homogeneous Polynomials on Real Normed Spaces |
| |
| Authors: | Pdraig Kirwan Yannis Sarantopoulos Andrew M Tonge |
| |
| Institution: | a University College, Galway, Ireland;b National Technical University, Zografou Campus 157 80, Athens, Greece;Department of Mathematics and Computer Science, Kent State University, P.O. Box 5190, Kent, Ohio, 44242, f1 |
| |
| Abstract: | IfPis a continuousm-homogeneous polynomial on a real normed space andPis the associated symmetricm-linear form, the ratio P/P always lies between 1 andmm/m!. We show that, as in the complex case investigated by Sarantopoulos (1987,Proc. Amer. Math. Soc.99, 340–346), there areP's for which P/P=mm/m! and for whichPachieves norm if and only if the normed space contains an isometric copy of ℓm1. However, unlike the complex case, we find a plentiful supply of such polynomials providedm4. |
| |
| Keywords: | |
| 本文献已被 ScienceDirect 等数据库收录！ |
|
