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比利时vs摩洛哥足彩 ,
university of california san diego

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functional analysis seminar

chris nelson

ucsd

a non-commutative nullstellensatz and positivstellensatz

abstract:

a natural question in real algebraic geometry is to ask, given polynomials $p$, $q$, and $r$, \begin{equation*} \tag{q} \label{eq:quest} \mbox{does} \quad q(x) \geq 0 \quad \mbox{and} \quad r(x) = 0 \quad \mbox{imply} \quad p(x) \geq 0\ \mbox{?} \end{equation*} in this talk i will focus on {\it free noncommutative} polynomials $p$, $q$, and $r$ and substitute matrices for the variables $x_j$. i will present an answer to a non-commutative version of (\ref{eq:quest}) which includes a non-commutative ``real nullstellensatz'' and ``positivstellensatz''.

host: bill helton

february 20, 2013

12:00 pm

ap&m 5829

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