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Fine spectra of upper triangular double-band matrices. (English) Zbl 1193.47006

Let c 0 be the space of all null sequences. Let c be the space of all convergent sequences. Let


be an upper triangular double-band infinite matrix. The operator on c 0 corresponding to the matrix V is denoted by (V,c 0 ). Then the point spectrum is σ p (V,c 0 )={λ:|λ-r|<|s|}, the residual spectrum σ r (V,c 0 )=, the continuous spectrum σ c (V,c 0 )={λ:|λ-r|=|s|}. Similarly, σ p (V,c), σ r (V,c) and σ c (V,c) are evaluated. Some applications of these results are given.

47A10Spectrum and resolvent of linear operators
47B37Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)