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Resolutions of the identity in certain Banach spaces. (English) Zbl 0718.46006
Summary: We prove the existence of projectional resolutions of the identity in a wide class of Banach spaces. This result is applied to the theory of generalized Markushevich bases, Asplund spaces and Banach spaces of continuous functions C(K) for scattered spaces K.

MSC:
46B15 Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces
46B20 Geometry and structure of normed linear spaces
47B15 Hermitian and normal operators (spectral measures, functional calculus, etc.)
46E15 Banach spaces of continuous, differentiable or analytic functions
46A50 Compactness in topological linear spaces; angelic spaces, etc.
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