An extension of Putnam-Fuglede theorem for hyponormal operators. (English) Zbl 0591.47020
Let \(S\in B(H)\) and \(T^*\in B(K)\) be hyponormal and assume \(C^ n(S,T)A=0\) for some \(A\in B(K,H)\), where \(C^ n(S,T)\) denotes n times application of the commutator C(S,T):\( B(K,H)\to B(K,H)\) defined by \(C(S,T)A=SA-AT\). Then \(C(S,T)A=C(S^*,T^*)A=0\). The result can be extended to a larger class of operators.
MSC:
| 47B20 | Subnormal operators, hyponormal operators, etc. |
| 47B47 | Commutators, derivations, elementary operators, etc. |
References:
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