Characters and Properties of Partial Orders of Operators
Received:December 19, 2005  Revised:December 10, 2006
Key Words: operator block matrice   operator partial order   special operator  
Fund Project:the National Natural Science Foundation of China (10571113); the Science Foundation of Xi’an University of Architecture & Technology (JC0621); the Science Young Foundation of Xi’an University of Architecture & Technology (QN0710).
Author NameAffiliation
PANG Yong-feng College of Mathematics and Information Science, Shaanxi Normal University, Shaanxi 710062, China
Department of Mathematics, Xi'an University of Architecture and Technology, Shaanxi 710055, China 
DU Hong-ke College of Mathematics and Information Science, Shaanxi Normal University, Shaanxi 710062, China 
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Abstract:
      We define four types of relations of two operators on Hilbert space: star, left-star, right-star and minus orders, respectively. Using the method of operator block matrices, we give the geometric characterizations of these orders. We prove that these orders are realy partial orders. Furthermore, we give relationships among these operator partial orders and their properties.
Citation:
DOI:10.3770/j.issn:1000-341X.2007.04.037
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