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Continuous spectrum, point spectrum and residual spectrum of operator matrices. (English) Zbl 1197.47013
Let M C denote a 2×2 upper triangular operator matrix of the form M C =AC0B, which is acting on the sum of Banach spaces XY or Hilbert spaces HK. The authors of this paper characterize the sets CB(Y,X) σ c (M C ), CB(K,H) σ p (M C ) and CB(K,H) σ r (M C ), where σ c (·), σ p (·) and σ r (·) denote the continuous spectrum, the point spectrum and the residual spectrum, respectively.
MSC:
47A10Spectrum and resolvent of linear operators
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