Subscalarity of operator transforms | Zendy

Jung Sungeun | Zendy; Ko Eungil | Zendy; Park Shinhae | Zendy

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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.

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