Korean J. Math. Vol. 22 No. 1 (2014) pp.85-89
DOI: https://doi.org/10.11568/kjm.2014.22.1.85

On $k$-quasi-class $A$ contractions

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Published: Mar 27, 2014
Mathematics Subject Classification:
47B20, 47A10

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In Ho Jeon
Seoul National University of Education
In Hyoun Kim
Incheon National University

Abstract

A bounded linear Hilbert space operator $T$ is said to be $k$-quasi-class $A$ operator if it satisfy the operator inequality ${T^*}^k|T^2|T^k\ge {T^*}^k|T|^2T^k$ for a non-negative integer $k$. It is proved that if $T$ is a $k$-quasi-class $A$ contraction, then either $T$ has a nontrivial invariant subspace or $T$ is a proper contraction and the nonnegative operator $D={T^*}^k(|T^2|-|T|^2)T^k$ is strongly stable.


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Supporting Agencies

This work of the second author was supported by the Incheon National University Grant in 2012.

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