Invertible completions of <IMG ALIGN=MIDDLE HEIGHT=24 WIDTH=43> upper triangular operator matrices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

Invertible completions of upper triangular operator matrices

Authors:	Jin Kyu Han Hong Youl Lee Woo Young Lee

Affiliation:	Department of Mathematics Education, Mokwon University, Daejon 301-719, Korea Hong Youl Lee ; Department of Mathematics, Woosuk University, Wanju-gun, Cheonbuk 565-800, Korea Woo Young Lee ; Department of Mathematics, Sung Kyun Kwan University, Suwon 440-746, Korea

Abstract:	In this note we prove that if $begin{equation}M_{C}=left (begin{smallmatrix}A&C 0&Bend{smallmatrix} right) end{equation}$ is a upper triangular operator matrix acting on the Banach space , then $M_{C}$ is invertible for some if and only if and satisfy the following conditions: (i) is left invertible; (ii) is right invertible; (iii) $X/A(X)cong B^{-1}(0)$ . Furthermore we show that $sigma (A)cup sigma (B)=sigma (M_{C})cup W$ , where is the union of certain of the holes in $sigma (M_{C})$ which happen to be subsets of .

Keywords:	Spectrum regular $2times 2$ upper triangular operator matrices

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