Open AccessTrace class operators via OPV-frames
Author(s) -
Ruchi Bhardwaj,
Soumya Sharma,
S. K. Kaushik
Publication year - 2021
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2113353b
Subject(s) - nuclear operator , mathematics , trace (psycholinguistics) , trace class , hilbert space , operator (biology) , pure mathematics , class (philosophy) , compact operator on hilbert space , space (punctuation) , bounded function , type (biology) , algebra over a field , mathematical analysis , compact operator , finite rank operator , computer science , extension (predicate logic) , banach space , linguistics , philosophy , repressor , artificial intelligence , chemistry , ecology , biology , operating system , biochemistry , transcription factor , programming language , gene
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.
Accelerating Research
Robert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom
Address
John Eccles HouseRobert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom