Geodesic
Tensor products of operators—strong stability andp-hyponormality
Glasgow mathematical journal, Tome 42 (2000) no. 3, pp. 371-381

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We say that the operator T ona Hilbert space H into itself is strongly stable if \left\VertT^nx\right\Vert →0 as n→∞, for allx∈H. If T is a contraction, then T issaid to be cs-stable if T has C_0 completelynon-unitary part. This note considers the strong stability of operators A⊗Band the p-hyponormality of operators A⊗B. It is shown that thecontraction A⊗B is cs-stable if and only if so are the contractionscA and c^{−1}B for some scalar c andA⊗B is p-hyponormal if and only if A andB are. We also characterize p-hyponormal A⊗B forwhich the commutator |A⊗B|_{2p}−|A^*⊗B^*|^{2p} iscompact. 
Duggal, B.P. Tensor products of operators—strong stability andp-hyponormality. Glasgow mathematical journal, Tome 42 (2000) no. 3, pp. 371-381. doi: 10.1017/S0017089500030068
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