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Author:

Zhang, Xiao-Li (Zhang, Xiao-Li.) | Li, Yun-Zhang (Li, Yun-Zhang.) (Scholars:李云章)

Indexed by:

Scopus SCIE

Abstract:

It is well known that there are two approaches applicable in constructing frames starting from one fixed frame. One is based on l(2)-operator portraits by which, using a suitable bounded linear operator on l(2), one can construct an arbitrary frame from one fixed frame. The other is based on perturbation that allows suitable perturbing a frame leaving a frame. The study of Hilbert-Schmidt frames (HS-frames) has interested some mathematicians in recent years. This paper addresses l(2)-operator portraits and perturbations in the setting of HS-frames. We prove that the portrait of a HS-frame under a bounded invertible operator on l(2) is still a HS-frame; present a sufficient condition on bounded operators on l(2) which transform an l(2)-decomposable HS-frame into another HS-frame (HS-Riesz basis, HS-frame sequence and HS-Riesz sequence); and prove that suitable perturbing a HS-frame sequence (HS-Riesz sequence) leaves a HS-frame sequence (HS-Riesz sequence). Finally, using these results we recover some conclusions on frames.

Keyword:

Frame HS-Riesz sequence HS-frame HS-frame sequence HS-Riesz basis

Author Community:

  • [ 1 ] [Zhang, Xiao-Li]Beijing Univ Technol, Fac Sci, Dept Math, Beijing 100124, Peoples R China
  • [ 2 ] [Li, Yun-Zhang]Beijing Univ Technol, Fac Sci, Dept Math, Beijing 100124, Peoples R China

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Source :

BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY

ISSN: 0126-6705

Year: 2022

Issue: 6

Volume: 45

Page: 3197-3223

1 . 2

JCR@2022

1 . 2 0 0

JCR@2022

ESI Discipline: MATHEMATICS;

ESI HC Threshold:20

JCR Journal Grade:2

CAS Journal Grade:3

Cited Count:

WoS CC Cited Count: 7

SCOPUS Cited Count: 6

ESI Highly Cited Papers on the List: 0 Unfold All

WanFang Cited Count:

Chinese Cited Count:

30 Days PV: 12

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