On k-quasi-class A contractions
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A bounded linear Hilbert space operator T is said to be k-quasi-class A operator if it satisfy the operator inequality T*k|T2|Tk ge T*k|T|2Tk 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(|T2|-|T|2)Tk is strongly stable.
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|T2|Tk ge T*k|T|2Tk 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(|T2|-|T|2)Tk is strongly stable.
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