Involutive operator algebras
- 18 Downloads
Examples of operator algebras with involution include the operator \(*\)-algebras occurring in noncommutative differential geometry studied recently by Mesland, Kaad, Lesch, and others, several classical function algebras, triangular matrix algebras, (complexifications) of real operator algebras, and an operator algebraic version of the complex symmetric operators studied by Garcia, Putinar, Wogen, Zhu, and others. We investigate the general theory of involutive operator algebras, and give many applications, such as a characterization of the symmetric operator algebras introduced in the early days of operator space theory.
KeywordsOperator algebras Involution Accretive operator Ideal Hereditary subalgebra Interpolation Complex symmetric operator
Mathematics Subject ClassificationPrimary 46K50 46L52 47L07 47L30 47L75 Secondary 32T40 46J15 46L07 46L85 47B44 47L25 47L45
This project grew out of , and we thank Jens Kaad and Bram Mesland for several ideas and perspectives learned there. We also thank Stephan Garcia–whose work on complex symmetric operators has influenced some results in our paper–for helpful conversations, and also Elias Katsoulis.
- 4.Bercovici, H.: Operator Theory and Arithmetic in \(H^\infty \), Mathematical Surveys and Monographs, 26. American Mathematical Society, Providence, RI (1988)Google Scholar
- 8.Blecher, D.P.: Generalization of C*-algebra methods via real positivity for operator and Banach algebras, In “Operator algebras and their applications: A tribute to Richard V. Kadison”. In: Doran, R.S., Park, E. (eds.) Contemporary Mathematics, vol. 671, pp. 35–66. American Mathematical Society, Providence, RI (2016)Google Scholar
- 20.Blecher, D. P., Wang, Z.: Jordan operator algebras revisited, Preprint 2018, to appear, Mathematische NachrichtenGoogle Scholar
- 31.Pisier, G.: Introduction to operator space theory, London Math. Soc. Lecture Note Series, 294, Cambridge University Press, Cambridge (2003)Google Scholar
- 34.Wang, Z.: Theory of Jordan operator algebras and operator \(^*\)-algebras, PhD thesis University of Houston (2019)Google Scholar