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http://dx.doi.org/10.11568/kjm.2014.22.1.85

ON k-QUASI-CLASS A CONTRACTIONS  

Jeon, In Ho (Department of Mathematics Education Seoul National University of Education)
Kim, In Hyoun (Department of Mathematics Incheon National University)
Publication Information
Korean Journal of Mathematics / v.22, no.1, 2014 , pp. 85-89 More about this Journal
Abstract
A bounded linear Hilbert space operator T is said to be k-quasi-class A operator if it satisfy the operator inequality $T^{*k}{\mid}T^2{\mid}T^k{\geq}T^{*k}{\mid}T{\mid}^2T^k$ 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 $D=T^{*k}({\mid}T^2{\mid}-{\mid}T{\mid}^2)T^k$ is strongly stable.
Keywords
k-quasi-class $\mathcal{A}$ operator; k-quasi-class $\mathcal{A}$ contraction; proper contraction; strongly stable;
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