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Funktsional'nyi Analiz i ego Prilozheniya, 2021, Volume 55, Issue 3, Pages 62–74
DOI: https://doi.org/10.4213/faa3835 (Mi faa3835) 		 
On R-dual of type III in Hilbert spaces

H. F\"uhra, J. Cheshmavarb, A. Akbarniab

a Lehrstuhl A für Mathematik, RWTH Aachen University, Aachen, Germany
b Department of Mathematics, Payame Noor University, Tehran, Iran
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DOI: https://doi.org/10.4213/faa3835
Abstract: Following work by Casazza, Kutyniok, and Lammers and its development by Stoeva and Christensen, we provide some novel characterizations of R-dual sequences of type III in Hilbert spaces. We systematically extend the construction procedure by basing it on a choice of an antiunitary involution. For certain classes of R-duals of type III, we derive a representation of the associated frame operator in terms of spectral measures.
Keywords: frames, Riesz sequence, Riesz basis, spectral representation, R-dual of type I, R-dual of type III.
Received: 18.08.2020
Revised: 14.03.2021
Accepted: 15.03.2021
English version:
Functional Analysis and Its Applications, 2021, Volume 55, Issue 3, Pages 226–235
DOI: https://doi.org/10.1134/S0016266321030059
Bibliographic databases:
Document Type: Article
UDC: 517.982
Language: Russian
Citation: H. Führ, J. Cheshmavar, A. Akbarnia, “On R-dual of type III in Hilbert spaces”, Funktsional. Anal. i Prilozhen., 55:3 (2021), 62–74; Funct. Anal. Appl., 55:3 (2021), 226–235
Citation in format AMSBIB
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\pages 62--74
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    		Функциональный анализ и его приложения Functional Analysis and Its Applications
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