, Volume 255, Issue 3, pp 579-596
Date: 23 Aug 2006

Strong majorization in a free ✱-algebra

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Abstract

We study, in the spirit of modern real algebra, the interplay between left ideals of the free ∗-algebra \(\mathbb F\) with n generators, and their suitably defined zero sets; and similarly between quadratic submodules of \(\mathbb F\) and their positivity sets.

Partially supported by grants from the National Science Foundation and the Ford Motor Co.