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Subscalarity of operator transforms
Author(s) -
Jung Sungeun,
Ko Eungil,
Park Shinhae
Publication year - 2015
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201500037
Subject(s) - mathematics , polar decomposition , iterated function , operator (biology) , order (exchange) , shift operator , bounded operator , bounded function , pure mathematics , mathematical analysis , polar , compact operator , biochemistry , chemistry , physics , finance , repressor , astronomy , computer science , transcription factor , gene , programming language , economics , extension (predicate logic)
In this paper, we provide various connections between a bounded linear operator T and some of its transforms, namely the Aluthge transformT ̃ A , Duggal transformT ̃ D , and mean transform T ̂ . In particular, we show that under the condition that| T | U | T | = | T | 2 U where T = U | T | is the polar decomposition, if one of T ,T ̃ D , andT ̃ A is subscalar of finite order, then T ̂ is also subscalar of finite order. As an application, we find subscalar operator matrices. We also give several spectral relations. Finally, we provide an equivalent condition under which a weighted shift has a hyponormal iterated mean transform.