MA 343: Complex analytic techniques in operator theory
Prerequisite courses: MA 223
Ando dilation of a commuting pair of contractions, Distinguished varieties of the bidisc, Description of all distinguished varieties, Construction of a distinguished variety corresponding to a pair of commuting matrices, Sharpening of Ando’s inequality, Extending the sharpened Ando inequality to operators with finite dimensional defect spaces, The extension property, Holomorphic retracts.
Suggested books and references:
T. Ando, On a pair of commutative contractions, Acta Sci. Math. (Szeged) 24 (1963) 88–90..
Agler, Jim and McCarthy, John E., Distinguished varieties., Acta Math. 194 (2005), no. 2, 133–153..
Das, B. Krishna and Sarkar, Jaydeb, Ando dilations, von Neumann inequality, and distinguished varieties., J. Funct. Anal. 272 (2017), no. 5, 2114–2131..