Weak semicontinuity for unbounded operators
Bull. Korean Math. Soc. 1997 Vol. 34, No. 3, 447-457
Hyoungsoon Kim
Yonsei University
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 $\and$ 3.27] for unbounded operators.
Keywords : semicontinuity, unbounded operators
MSC numbers : 46L85, 47D40
Downloads: Full-text PDF  


Copyright © Korean Mathematical Society. All Rights Reserved.
The Korea Science Technology Center (Rm. 411), 22, Teheran-ro 7-gil, Gangnam-gu, Seoul 06130, Korea
Tel: 82-2-565-0361  | Fax: 82-2-565-0364  | E-mail: paper@kms.or.kr   | Powered by INFOrang Co., Ltd