Joint Similarities And Parameterizations For Naimark Complementary Frames

Keywords

Dilations; Dual frames; Dual Riesz basis; Joint similarity

Abstract

It is known that the Naimark complementary frames for a given frame are not necessarily unique up to the similarity. In this paper we introduce the concept of joint complementary frame pairs for a given dual frame pair, and prove that they are unique up to the joint similarity. As an application, we give a necessary and sufficient condition under which two Naimark complementary frames are similar. For different pairs of dual frames, we present an operator parameterization for their joint complementary frame pairs.

Publication Date

6-1-2018

Publication Title

Journal of Mathematical Analysis and Applications

Volume

462

Issue

1

Number of Pages

148-156

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.jmaa.2018.01.072

Socpus ID

85044590348 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/85044590348

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