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Positivity

pp 1–41 | Cite as

Involutive operator algebras

  • David P. BlecherEmail author
  • Zhenhua Wang
Article
  • 18 Downloads

Abstract

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.

Keywords

Operator algebras Involution Accretive operator Ideal Hereditary subalgebra Interpolation Complex symmetric operator 

Mathematics Subject Classification

Primary 46K50 46L52 47L07 47L30 47L75 Secondary 32T40 46J15 46L07 46L85 47B44 47L25 47L45 

Notes

Acknowledgements

This project grew out of [10], 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.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of HoustonHoustonUSA

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