Continuous spectrum, point spectrum and residual spectrum of operator matrices |
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Authors: | Shifang Zhang Zhenying Wu |
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Institution: | a Department of Mathematics, Fujian Normal University, Fuzhou 350007, PR China b Department of Mathematics, Zhejiang University, Hangzhou 310027, PR China |
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Abstract: | Let MC denote a 2 × 2 upper triangular operator matrix of the form , which is acting on the sum of Banach spaces X⊕Y or Hilbert spaces H⊕K. In this paper, the sets and ?C∈B(K,H)σr(MC) are, respectively, characterized completely, where σc(·) denotes the continuous spectrum, σp(·) denotes the point spectrum and σr(·) denotes the residual spectrum. Moreover, some corresponding counterexamples are given. |
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Keywords: | Operator matrices The continuous spectrum The point spectrum The residual spectrum |
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