Abstract
The free automorphisms of a class of Reinhardt free spectrahedra are trivial.
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J. William Helton, I. Klep, S. McCullough, J. Volčič, Bianalytic free maps between spectrahedra and spectraballs. J. Funct. Anal. 278(11), 15 (2020). https://doi.org/10.1016/j.jfa.2020.108472
R. Horn, C. Johnson, Matrix Analysis, 2nd edn. (Cambridge University Press, Cambridge, 2013)
G. Blekherman, P. Parrilo, R. Thomas (eds.), Semidefinite Optimization and Convex Algebraic Geometry. MPS-SIAM Series on Optimization, 13 (SIAM, 2013)
M.C. De Oliveira, J.W. Helton, Computer algebra tailored to matrix inequalities incontrol. Int. J. Control 79(11), 1382–1400 (2006). https://doi.org/10.1080/00207170600725529
M. de Oliveira, J.W. Helton, S. McCullough, M. Putinar, Engineering systems and free semi-algebraic geometry, in Emerging Applications of Algebraic Geometry. The IMA Volumes in Mathematics and its Applications, vol. 149 (Springer, New York, 2009), pp. 17–61
H. Wolkowicz, R. Saigal, L. Vandenberghe (eds.), in Handbook of Semidefinite Programming: Theory, Algorithms, and Applications. International Series in Operations Research & Management Science, vol. 27 (Springer, Berlin, 2012)
R. Skelton, T. Iwasaki, K. Grigoriadis, in A Unified Algebraic Approach to Linear Control Design (Taylor & Francis, London, 1997)
D. Kalyuzhnyi-Verbovetskiĭ, V. Vinnikov, in Foundations of Free Noncommutative Function Theory. Mathematical Surveys and Monographs, vol. 199 (American Mathematical Society, Providence, 2014)
S. McCullough, N. Tuovila, in Reinhardt Free Spectrahedra. Linear Algebra Appl. 640, 91–117 (2022) ar**v:2012.02289 http://www.ar**v:2012.02289
M. Jarnicki, P. Pflug, in First Steps in Several Complex Variables: Reinhardt Domains. EMS Textbooks in Mathematics (European Mathematical Society (EMS), Zürich, 2008)
G. Popescu, Free holomorphic automorphisms of the unit ball of B(H)n. J. Reine Angew. Math. 638, 119–168 (2010)
J. McCarthy, R. Timoney, Non-commutative automorphisms of bounded non-commutative domains. Proc. R. Soc. Edin. Sect. A 146, 1037–1045 (2016)
M. Augat, I. Klep, B. Helton, S. McCullough, Bianalytic maps between free spectrahedra. Math. Ann. 371(1–2), 883–959 (2018)
J.W. Helton, I. Klep, S. McCullough, Free analysis, convexity and LMI domains, in Mathematical Methods in Systems, Optimization, and Control. Operator Theory: Advances and Applications, vol. 222 (Birkhäuser/Springer Basel AG, Basel, 2012), pp. 195–219
J.W. Helton, I. Klep, S. McCullough, Proper analytic free maps. J. Funct. Anal. 260(5), 1476–1490 (2011)
E. Evert, B. Helton, S. McCullough, I. Klep, Circular free spectrahedra. J. Math. Anal. Appl. 445(1), 1047–1070 (2017)
J.W. Helton, S. McCullough, Every convex free basic semi-algebraic set has an LMI representation. Ann. Math. 176(2), 979–1013 (2012)
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McCullough, S. (2023). Automorphisms of Hyper-Reinhardt Free Spectrahedra. In: Alpay, D., Behrndt, J., Colombo, F., Sabadini, I., Struppa, D.C. (eds) Recent Developments in Operator Theory, Mathematical Physics and Complex Analysis. Operator Theory: Advances and Applications, vol 290. Birkhäuser, Cham. https://doi.org/10.1007/978-3-031-21460-8_7
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