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L(n)-HYPONORMALITY: A MISSING BRIDGE BETWEEN SUBNORMALITY AND PARANORMALITY

Part of: Special classes of linear operators

Published online by Cambridge University Press:  01 April 2010

IL BONG JUNG ,
SUN HYUN PARK  and
JAN STOCHEL
IL BONG JUNG*
Affiliation:
Department of Mathematics, Kyungpook National University, Daegu 702-701, Korea (email: ibjung@knu.ac.kr)
SUN HYUN PARK
Affiliation:
Department of Mathematics, Kyungpook National University, Daegu 702-701, Korea (email: sm1907s4@hanmail.net)
JAN STOCHEL
Affiliation:
Instytut Matematyki, Uniwersytet Jagielloński, ul. Łojasiewicza 6, PL-30348 Kraków, Poland (email: Jan.Stochel@im.uj.edu.pl)
*
✉For correspondence; e-mail: ibjung@knu.ac.kr
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Abstract

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A new notion of L(n)-hyponormality is introduced in order to provide a bridge between subnormality and paranormality, two concepts which have received considerable attention from operator theorists since the 1950s. Criteria for L(n)-hyponormality are given. Relationships to other notions of hyponormality are discussed in the context of weighted shift and composition operators.

Keywords

subnormal operatorparanormal operatorL(n)-hyponormal operatorweighted shift operatorcomposition operator

MSC classification

Secondary: 47B20: Subnormal operators, hyponormal operators, etc. 47B37: Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 88 , Issue 2 , April 2010 , pp. 193 - 203
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2010

Footnotes

The work of the first author was supported by a Korea Science and Engineering Foundation (KOSEF) grant funded by the Korea government (No. R01-2008-000-20088-0). The work of the third author was supported by MNiSzW grant N201 026 32/1350.

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