Open AccessTrace class operators via OPV-frames
Author(s) -
Ruchi Bhardwaj,
Sharda 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.