학술저널
Extreme Positive Operators from 2×2 to 3×3 Hermitian Matrices
- 충청수학회
- Journal of the Chungcheong Mathematical Society
- Volume 4, No. 1
-
1991.0611 - 38 (28 pages)
- 0
Let En be the real ordered space of all n×n Hermitian Matrices and let T be a positive linear operator from E₂ to E₃. We prove in this paper that T is extreme if and only if T is unitarily equivalent to a map of the form Sz for some z ∈ C² where Sz is defined by Sz(xx*) = ww*, wi = xizi for i = 1, 2 and w₃ = 0.
ABSTRACT
1. Introduction
2. When r(T(xx*)) = 3 for Some x ∈ C²
3. When r(T(xx*)) ≤ 2 for Every x ∈ C²
4. When r(T(xx*)) = 2 for All Nonzero x ∈ C²
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