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Subscalarity of operator transforms

Title
Subscalarity of operator transforms
Authors
Jung, SungeunKo, EungilPark, Shinhae
Ewha Authors
고응일
SCOPUS Author ID
고응일scopus
Issue Date
2015
Journal Title
MATHEMATISCHE NACHRICHTEN
ISSN
0025-584XJCR Link1522-2616JCR Link
Citation
vol. 288, no. 17-18, pp. 2042 - 2056
Keywords
Mean transformAluthge transformDuggal transformsubscalar operatorinvariant subspace
Publisher
WILEY-V C H VERLAG GMBH
Indexed
SCI; SCIE; SCOPUS WOS scopus
Abstract
In this paper, we provide various connections between a bounded linear operator T and some of its transforms, namely the Aluthge transform (T) over tilde (A), Duggal transform (T) over tilde (D), and mean transform (T) over cap. In particular, we show that under the condition that vertical bar T vertical bar U vertical bar T vertical bar = vertical bar T vertical bar U-2 where T = U vertical bar T vertical bar is the polar decomposition, if one of T, (T) over tilde (D), and (inverted perpendicular) over tilde (A) is subscalar of finite order, then (T) over cap 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. (C) 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
DOI
10.1002/mana.201500037
Appears in Collections:
자연과학대학 > 수학전공 > Journal papers
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