Equivalent conditions for decomposable operators

Lange, Ridgley

doi:10.1090/S0002-9939-1981-0612729-9

Equivalent conditions for decomposable operators
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Proc. Amer. Math. Soc. 82 (1981), 401-406 Request permission

Abstract:

Several new characterizations of an arbitrary decomposable operator on Banach space are given; for example, one of these is in terms of spectral conditions on an arbitrary invariant subspace, while another uses the spectral manifold ${X_T}({G^ - })$ (rather than ${X_T}(F)$). From these results a short proof of Frunzǎ’s duality theorem is derived. Finally we give sufficient conditions that the predual of a decomposable operator is of the same class.

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