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On some local spectral theory and bounded local resolvent of operator matrices. (English) Zbl 1487.47012

The authors extend and generalize some results in local spectral theory for upper triangular operator matrices acting on a Banach space to upper triangular operator matrices with unbounded entries. The authors give sufficient conditions on its diagonal entries which ensure the boundedness of the local resolvent function of bounded upper triangular operator matrices.

MSC:

47A11 Local spectral properties of linear operators
47A08 Operator matrices
47A53 (Semi-) Fredholm operators; index theories
47A10 Spectrum, resolvent
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