Annals of Functional Analysis
- Ann. Funct. Anal.
- Volume 6, Number 4 (2015), 226-246.
Geometry and operator theory on quaternionic Hilbert spaces
In this article, we study the geometry and operator theory on quaternionic Hilbert spaces. As it is well-known, Cowen--Douglas operators are a class of non-normal operators related to complex geometry on complex Hilbert spaces. Our purpose is to generalize this concept on quaternionic Hilbert spaces. At the beginning, we study a class of complex holomorphic curves which naturally induce complex vector bundles as sub-bundles in the product space of the base space and a quaternionic Hilbert space. Then we introduce quaternionic Cowen--Douglas operators and give their quaternion unitarily equivalent invariant related to the geometry of the holomorphic curves.
Ann. Funct. Anal., Volume 6, Number 4 (2015), 226-246.
First available in Project Euclid: 1 July 2015
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Hou, Bingzhe; Tian, Geng. Geometry and operator theory on quaternionic Hilbert spaces. Ann. Funct. Anal. 6 (2015), no. 4, 226--246. doi:10.15352/afa/06-4-226. https://projecteuclid.org/euclid.afa/1435764014