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Decomposition of operators with countable spectrum. (English) Zbl 0635.47034

Sufficient spectral conditions for the existence of a spectral decomposition of an operator T defined on a Banach space X, with countable spectrum are given. We apply the results to obtain the West decomposition of certain Riesz operators.

MSC:

47B40 Spectral operators, decomposable operators, well-bounded operators, etc.
47B06 Riesz operators; eigenvalue distributions; approximation numbers, \(s\)-numbers, Kolmogorov numbers, entropy numbers, etc. of operators
47A70 (Generalized) eigenfunction expansions of linear operators; rigged Hilbert spaces
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