Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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Weak semicontinuity for unbounded operators

  • Kim, Hyoungsoon (Department of Mathematics, Yonsei University, Kangwondo 220-710)
  • Published : 1997.08.01
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Abstract

Let A be a $C^*$-algebra and $A^**$ its enveloping von Neumann algebra. Pedersen and Akemann developed four concepts of lower semicontinuity for elements of $A^**$. Later, Brown suggested using only three classes: strongly lsc, middle lsc, and weakly lsc. In this paper, we generalize the concept of weak semicontinuity [1, 3] to the case of unbounded operators affiliated with $A^**$. Also we consider the generalized version of the conditions of the Brown's theorem [3, Proposition 2.2 & 3.27] for unbounded operators.

Keywords

References

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