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Remarks on Naimark dilation theorem

Part of: Nontrigonometric harmonic analysis Normed linear spaces and Banach spaces; Banach lattices

Published online by Cambridge University Press:  28 November 2023

Sergiusz Kużel Open the ORCID record for Sergiusz Kużel [Opens in a new window]
Sergiusz Kużel*
Affiliation:
AGH University of Science and Technology, al. A. Mickiewicza 30, Kraków, 30-059, Poland
*
e-mail: [email protected]
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Abstract

Although Naimark dilation theorem was originally stated in 1940, it still finds many important applications in various areas. The objective of this paper is to introduce a method for explicitly constructing the vectors of complementary frames in the Naimark dilation theorem, specifically in cases where the initial Parseval frame contains a Riesz basis as a subset. These findings serve as a foundation for the construction of dual frames.

Keywords

Naimark dilation theoremParseval framedual frameRiesz basis

MSC classification

Primary: 46B15: Summability and bases
Secondary: 42C15: General harmonic expansions, frames
Type
Article
Information
Canadian Mathematical Bulletin , Volume 67 , Issue 2 , June 2024 , pp. 469 - 477
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of The Canadian Mathematical Society

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Footnotes

This work was partially supported by the Faculty of Applied Mathematics AGH UST statutory tasks within subsidy of the Ministry of Science and Higher Education of Poland.

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