C* - algebras 上的正映射及數值域

Abstract

在這篇論文中, 我們對C* - algebras 上的正映射, n-正映射, 及完全正 映射做了一些研究. 此外, 藉由Stinespring's Theorem 及 Arveson's Extension Theorem 去研究 C* - algebras 上元素的矩陣域. 最後,經由 先前對正映射函數的研究結果, 發現 Hilbert空間上的算子其矩陣域和一 般 n-數值域的關係. 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.