On \(\ast\)-paranormal contractions and properties for \(\ast\)-class \(A\) operators. (English) Zbl 1234.47008
Summary: An operator \(T\in B(\mathcal{H})\) is called a \(\ast\)-class \(\mathcal{A}\) operator if \(|T^{2}|\geq|T^\ast |^2\), and \(T\) is said to be \(\ast\)-paranormal if \(\| T^{\ast}x\| ^2\leq\| T^2x\|\) for every unit vector \(x\) in \(\mathcal{H}\). In this paper, we show that \(\ast\)-paranormal contractions are the direct sum of a unitary and a \(C_{.0}\) completely non-unitary contraction. Also, we consider the tensor products of \(\ast\)-class \(\mathcal{A}\) operators.
MSC:
| 47B20 | Subnormal operators, hyponormal operators, etc. |
| 47A10 | Spectrum, resolvent |
| 47A80 | Tensor products of linear operators |
Keywords:
\(\ast\)-class \(A\) operators; \(\ast\)-paranormal operators; \(C_{.0}\)-contraction; tensor productReferences:
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