Invariant subspaces for Banach space operators with an annular spectral set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

Invariant subspaces for Banach space operators with an annular spectral set

Authors:	Onur Yavuz

Affiliation:	Department of Mathematics, Indiana University, Rawles Hall, Bloomington, Indiana 47405

Abstract:	Consider an annulus $Omega={zinmathbb{C}:r_ {0}<vert zvert<1}$ for some $0<r_{0}<1$ , and let be a bounded invertible linear operator on a Banach space whose spectrum contains . Assume there exists a constant such that and $Vert p(r_0T^{-1})Vertleq K sup{vert p(lambda)vert:vertlambdavertleq 1}$ for all polynomials . Then there exists a nontrivial common invariant subspace for $T^{}$ and ${T^{}}^{-1}$ .

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