Completely positive interpolations and preservers on tensor products of low rank matrices
博士 === 國立中山大學 === 應用數學系研究所 === 102 === In this thesis, we will consider the following problems: (i). We study linear maps of matrix algebras, which preserve some spectral functions on a small subset of mn x mn matrices. (ii). We study completely positive interpolations between normal matrices (ope...
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| Format: | Others |
| Language: | en_US |
| Published: |
2014
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| Online Access: | http://ndltd.ncl.edu.tw/handle/14395807928517454426 |
| Summary: | 博士 === 國立中山大學 === 應用數學系研究所 === 102 === In this thesis, we will consider the following problems:
(i).
We study linear maps of matrix algebras, which preserve some spectral functions on a small
subset of mn x mn matrices.
(ii).
We study completely positive interpolations between normal matrices (operators) using
their spectrum and the Choi-Kraus form. We obtain a necessary and sufficient condition
for the existence of a completely positive interpolation in terms of conditions about
numerical ranges and dilations.
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