ON A CLASS OF OPERATORS RELATED TO PARANORMAL OPERATORS

ON A CLASS OF OPERATORS RELATED TO PARANORMAL OPERATORS

An operator $T{\in}L(H)$ is said to be p-paranormal if $$\parallel{\mid}T\mid^pU{\mid}T\mid^px{\parallel}x\parallel\geq\parallel{\mid}T\mid^px\parallel^2$$ for all $x{\in}H$ and p > 0, where $T=U{\mid}T\mid$ is the polar decomposition of T. It is easy that every 1-paranormal operator is paranormal, and every p-paranormal operator is paranormal for 0 < p < 1. In this note, we discuss some properties for p-paranormal operators.

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