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

In Ho Jeon, In Hyoun Kim

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.

Subject classification

47B20, 47A10

Sponsor(s)

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

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