Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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ON A CLASS OF OPERATORS RELATED TO PARANORMAL OPERATORS

  • Lee, Mi-Young (Department of Mathematics College of Natural Science Kyungpook National University) ;
  • Lee, Sang-Hun (Department of Mathematics College of Natural Science Kyungpook National University)
  • Published : 2007.01.31
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Abstract

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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