Completely positive interpolations of compact, trace-class and Schatten-p class operators

详细信息    查看全文

• 作者：Ming-Hsiu Hsu^a ; ^{hsumh@math.ncu.edu.tw" class="auth_mail} ; David Li-Wei Kuo^b ; ^{mpu.verilog@gmail.com" class="auth_mail} ; Ming-Cheng Tsai^b ; ^{mctsai2@gmail.com" class="auth_mail}
• 关键词：15B48 ; 15B51 ; 47L30 ; 81P68
• 刊名：Journal of Functional Analysis
• 出版年：15 August 2014
• 年：2014
• 卷：267
• 期：4
• 页码：1205-1240
• 全文大小：527 K

文摘

Extending Li and Poon's results on interpolation problems for matrices, we give characterizations of the existence of a completely positive linear map 桅_cp${桅}_{\mathrm{cp}}$ between compact (or Schatten-p   class) operators sending a particular operator A   to another B  . It is shown that such a map exists if a multiple of the numerical range of A   contains the numerical range of B  . Given two commutative families of compact (or Schatten-p   class) operators {A_伪}$\{A_{伪}\}$ and {B_伪}$\{B_{伪}\}$, we provide sufficient and necessary conditions to ensure that we can choose a completely positive interpolation 桅_cp${桅}_{\mathrm{cp}}$ to preserve trace and/or approximate units such that 桅_cp(A_伪)=B_伪${桅}_{\mathrm{cp}}(A_{伪})=B_{伪}$ for all 伪.