The Early History of the Ham Sandwich Theorem
The Early History of the Ham Sandwich Theorem
复制标题
火腿三明治定理的早期历史
DOI：
10.1080/00029890.2004.11920050
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
A. Zardecki
中科院分区：
文献类型：
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作者：
W. A. Beyer;A. Zardecki
证明设Sym(A)：={a A：a*=a，且设a属于Sym(A)。考虑A的子代数B，它包含a中的所有实系数多项式。则B包含在Sym(A)中。因此，B满足定理3.1的假设。由于B也是可交换的，所以B与R或C同构。因此，对于某些实数或复数，a=X11)。这表明Sym(A)本身与R或C同构。现在从文献[1]的引理2.1得出结论。0
Proof Let Sym(A) := {a A : a* = a), and let a belong to Sym(A). Consider the subalgebra B of A that comprises all polynomials in a with real coefficients. Then B is contained in Sym(A). Hence B satisfies hypotheses of Theorem 3.1. Since B is also commutative, B is isomorphic to R or C. Hence a = X1l for some real or complex number ). This shows that Sym(A) itself is isomorphic to R or C. Now the conclusion follows from Lemma 2.1 of [1]. 0