| 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
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| 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). |
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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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