Approximation by polynomials with nonnegative coefficients and the spectral theory of positive operators期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

按检索

Approximation by polynomials with nonnegative coefficients and the spectral theory of positive operators

Authors:	Roger D Nussbaum Bertram Walsh

Institution:	Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903-2101 ; Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903-2101

Abstract:	For $\Sigma$ a compact subset of $\mathbf{C}$ symmetric with respect to conjugation and $f: \Sigma \to \mathbf{C}$ a continuous function, we obtain sharp conditions on and $\Sigma$ that insure that can be approximated uniformly on $\Sigma$ by polynomials with nonnegative coefficients. For a real Banach space, $K \subseteq X$ a closed but not necessarily normal cone with $\overline{K - K} = X$ , and $A: X \to X$ a bounded linear operator with $AK] \subseteq K$ , we use these approximation theorems to investigate when the spectral radius $\text{\rm r}(A)$ of belongs to its spectrum $\sigma (A)$ . A special case of our results is that if is a Hilbert space, is normal and the 1-dimensional Lebesgue measure of $\sigma (i(A - A^{*}))$ is zero, then $\text{\rm r}(A) \in \sigma (A)$ . However, we also give an example of a normal operator $A = - U -\alpha I$ (where is unitary and $\alpha > 0$ ) for which $AK] \subseteq K$ and $\text{\rm r}(A) \notin \sigma (A)$ .

Keywords:	Polynomial approximation with nonnegative coefficients positive linear operators spectral radius

	点击此处可从《Transactions of the American Mathematical Society》浏览原始摘要信息
	点击此处可从《Transactions of the American Mathematical Society》下载免费的PDF全文

设为首页 | 免责声明 | 关于勤云 | 加入收藏