Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, especially operator theory, a paranormal operator is a generalization of a normal operator. More precisely, a bounded linear operator T on a complex Hilbert space H is said to be paranormal if:Every hyponormal operator (in particular, a subnormal operator, a quasinormal operator and a normal operator) is paranormal. If T is a paranormal, then Tn is paranormal. On the other hand, Halmos gave an example of a hyponormal operator T such that T2 isn't hyponormal. Consequently, not every paranormal operator is hyponormal.

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