A positivstellensatz for non-commutative polynomials

By Scott McCullough. 2004

138 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/aa99bd5f17ec586b88d0e8972338fd77cb0b8e44

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. J. William Helton
2. Gelu Popescu
3. Mihai Putinar
4. Nathanial P. Brown Narutaka Ozawa
5. Gilles Pisier
6. Adrian Ioana
7. Orr Shalit
8. W. Winter

In Applied Mathematics

1. Gelu Popescu
2. J. William Helton
3. Mihai Putinar
4. Nathanial P. Brown Narutaka Ozawa
5. Victor Vinnikov
6. Gilles Pisier
7. Dmitry S. Kaliuzhnyi-Verbovetskyi
8. Orr Shalit

In Mathematical Physics

1. Gelu Popescu
2. J. William Helton
3. Mihai Putinar
4. Nathanial P. Brown Narutaka Ozawa
5. Gilles Pisier
6. Adrian Ioana
7. Victor Vinnikov
8. Dmitry S. Kaliuzhnyi-Verbovetskyi

Citations in the corpus

• POSITIVE POLYNOMIALS IN SCALAR AND MATRIX VARIABLES, THE SPECTRAL THEOREM AND OPTIMIZATION (2006, background): “ (X1,...,Xg) is a tuple of operators on H, v ∈ H, and pj(X)v = 0 for all j, then q is in the left ideal generated by p1,...,pm. Proof (of Lemma). We sketch a proof based on an idea of G. Bergman, see [HM04a]. Let I be the left ideal generated by p1,...,pm in F = Rhx1,...,xgi. Define V to be the vecto”
• About the Connes Embedding Conjecture---Algebraic approaches--- (2012, methodology): “the C∗-algebraic aspect of noncommutative real algebraic geometry in terms of semi-pre-C∗-algebras. Specifically, we treat some easy parts of Positivstellens¨atze of Putinar ([Pu]), Helton–McCullough ([HM]), and Schmu¨dgen–Bakonyi–Timotin ([BT]). We then treat their tracial analogue by Klep– Schweigh”
• Matrix-J-unitary Non-commutative Rational Formal Power Series (2004, unknown): “, matrix-positivity of non-commutative polynomials (non-commutative Positivstellensatz) [29, 40, 31, 32], matrix-positivity of FPS kernels [34], matrix-convexity [21, 30].”
• Operator Theory on Noncommutative Domains (2007, unknown): “In a related area of research, we remark the work of Helton, McCullough, Putinar, and Vinnikov, on symmetric noncommutative polynomials ([48], [49], [51], [50], [52]), which contains a new type of engineering application.”
• Free holomorphic functions and interpolation (2007, methodology): “In related areas of research, we remark the work of Helton, McCullough, Putinar, and Vinnikov, on symmetric noncommutative polynomials ([13], [14], [15], [16]), and the work of Muhly and Solel on representations of tensor algebras over C correspondences (see [19], [20]).”