Positive Maps on C* - algebras and Numerical Ranges

• Main Authors: Ching-I Hsin, 辛靜宜
• Other Authors: Chikaung Pai
• Format: Others
• Language: en_US
• Published: 1994
• Online Access: http://ndltd.ncl.edu.tw/handle/32808126960202922739

碩士 === 國立交通大學 === 應用數學研究所 === 82 === In this paper, we study the positive, n-positive, and completely positive maps on C* - algebras. Our first objective is, pursuing the work of Stinespring and Arveson, to characterize the positive maps between Mn and C(X) and the extension theorem. Building upon Stinespring's theorem and Arveson's extension theorem, we then survey the matrix ranges of an element in a C* - algebra. Moreover, for a Hilbert space operator, we find the relation between its matrix range and its usual n-numerical range.