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April 2020 Some properties of solutions to the Riccati equations in connection with Bergman spaces
Junming Liu, Huayou Xie
Rocky Mountain J. Math. 50(2): 651-657 (April 2020). DOI: 10.1216/rmj.2020.50.651

Abstract

We investigate the properties of solutions to operator Riccati equations in connection with Bergman spaces. We characterize some necessary conditions for the solvability of the Riccati equation

X A X + X B C X D = 0

on the set τ of all Toeplitz operators on the Bergman spaces A α 2 ( 𝔻 ) . This extends the results of Karaev on Hardy space.

Citation

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Junming Liu. Huayou Xie. "Some properties of solutions to the Riccati equations in connection with Bergman spaces." Rocky Mountain J. Math. 50 (2) 651 - 657, April 2020. https://doi.org/10.1216/rmj.2020.50.651

Information

Received: 6 May 2019; Revised: 21 September 2019; Accepted: 30 September 2019; Published: April 2020
First available in Project Euclid: 29 May 2020

zbMATH: 07210986
MathSciNet: MR4104401
Digital Object Identifier: 10.1216/rmj.2020.50.651

Subjects:
Primary: ‎32A36‎, 47B35

Rights: Copyright © 2020 Rocky Mountain Mathematics Consortium

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Vol.50 • No. 2 • April 2020
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