Geodesic
Trace class operators via OPV-frames
Filomat, Tome 35 (2021) no. 13, p. 4353

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DOI

Trace class operators for quaternionic Hilbert spaces (QHS) were studied by Moretti and Oppio [18]. In this paper, we study trace class operators via operator valued frames (OPV-frames). We introduce OPV-frames in a right quaternionic Hilbert space H with range in a two sided quaternionic Hilbert space K and obtain various results including several characterizations of OPV-frames. Also, we obtain a necessary and sufficient condition for a bounded operator on a right QHS to be a trace class operator which generalizes a similar result by Attal [2]. Moreover, we construct a trace class operator on a two sided QHS. Finally, we study quaternionic quantum channels as completely positive trace preserving maps and obtain various Choi-Kraus type representations of quaternionic quantum channels using OPV-frames in quaternionic Hilbert spaces
DOI : 10.2298/FIL2113353B
Classification : 42C15, 42A38
Keywords: Frame, Quaternionic Hilbert spaces 
Ruchi Bhardwaj; S K Sharma; S K Kaushik. Trace class operators via OPV-frames. Filomat, Tome 35 (2021) no. 13, p. 4353 . doi: 10.2298/FIL2113353B
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     author = {Ruchi Bhardwaj and S K Sharma and S K Kaushik},
     title = {Trace class operators via {OPV-frames}},
     journal = {Filomat},
     pages = {4353 },
     year = {2021},
     volume = {35},
     number = {13},
     doi = {10.2298/FIL2113353B},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2113353B/}
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