Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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ON SPECTRAL CONTINUITIES AND TENSOR PRODUCTS OF OPERATORS

  • Kim, In Hyoun (Department of Mathematics University of Incheon)
  • Received : 2011.01.24
  • Accepted : 2011.02.23
  • Published : 2011.03.30
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Abstract

Let T be a bounded linear operator on a complex Hilbert space $\mathcal{H}$. An operator T is called class A operator if ${\left|{T^2}\right|}{\geq}{\left|{T^2}\right|}$ and is called class A(k) operator if $({T^*\left|T\right|^{2k}T})^{\frac{1}{k+1}}{\geq}{\left|T\right|}^2$. In this paper, we show that ${\sigma}$ is continuous when restricted to the set of class A operators and consider the tensor products of class A(k) operators.

Keywords

Acknowledgement

Supported by : University of Incheon

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