Some Properties of Operator Valued Frames in Quaternionic Hilbert Spaces

Guoqing Hong () and Pengtong Li
Additional contact information
Guoqing Hong: College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, China
Pengtong Li: Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

Mathematics, 2022, vol. 11, issue 1, 1-9

Abstract: Quaternionic Hilbert spaces play an important role in applied physical sciences especially in quantum physics. In this paper, the operator valued frames on quaternionic Hilbert spaces are introduced and studied. In terms of a class of partial isometries in the quaternionic Hilbert spaces, a parametrization of Parseval operator valued frames is obtained. We extend to operator valued frames many of the properties of vector frames on quaternionic Hilbert spaces in the process. Moreover, we show that all the operator valued frames can be obtained from a single operator valued frame. Finally, several results for operator valued frames concerning duality, similarity of such frames on quaternionic Hilbert spaces are presented.

Keywords: frame; quaternionic Hilbert space; operator valued frame (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/1/188/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/1/188/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2022:i:1:p:188-:d:1019376

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().