• Corpus ID: 251066581

Approximate Pythagoras Numbers on $*$-algebras over $\mathbb{C}$

@inproceedings{Abbasi2021ApproximatePN,
  title={Approximate Pythagoras Numbers on \$*\$-algebras over \$\mathbb\{C\}\$},
  author={Paria Abbasi and Sander Gribling and Andreas Klingler and Tim Netzer},
  year={2021}
}
. The Pythagoras number of a sum of squares is the shortest length among its sums of squares representations. In many algebras, for example real polynomial algebras in two or more variables, there exists no upper bound on the Pythagoras number for all sums of squares. In this paper, we study how Pythagoras numbers in ∗ -algebras over C behave with respect to small perturbations of elements. More pre-cisely, the approximate Pythagoras number of an element is the smallest Pythagoras number among… 
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