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On the essential spectrum of matrix operators. (English. Russian original) Zbl 0871.47005

Math. Notes 58, No. 6, 1359-1362 (1995); translation from Mat. Zametki 58, No. 6, 945-949 (1995).
Let \(L=\left[\begin{smallmatrix} A & B\\ C & D\end{smallmatrix}\right]\) be an unbounded matrix operator acting on a Banach space. It is shown in the present paper that, under some suitable assumption, \(L\) is closable if and only if \(S(\mu)\) is and the essential spectrum of \(L\) is the union of that of \(A\) and \(S(\mu)\).

MSC:

47A10 Spectrum, resolvent
47B37 Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
47A05 General (adjoints, conjugates, products, inverses, domains, ranges, etc.)
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