This is an announcement for the paper "Notes on the geometry of space of polynomials" by Han Ju Lee.

Abstract: We show that the symmetric injective tensor product space $\hat{\otimes}_{n,s,\varepsilon}E$ is not complex strictly convex if $E$ is a complex Banach space of $\dim E \ge 2$ and if $n\ge 2$ holds. It is also reproved that $\ell_\infty$ is finitely represented in $\hat{\otimes}_{n,s,\varepsilon}E$ if $E$ is infinite dimensional and if $n\ge 2$ holds, which was proved in the other way by Dineen.

Archive classification: math.FA

Mathematics Subject Classification: 46B20

The source file(s), Notes-on-geometry-polynomials-revised.tex: 12189 bytes, is(are) stored in gzipped form as 0708.0331.gz with size 4kb. The corresponding postcript file has gzipped size 53kb.

Submitted from: hahnju@postech.ac.kr

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http://front.math.ucdavis.edu/0708.0331

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http://arXiv.org/abs/0708.0331

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