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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.
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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
Affiliated Colleges: