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 − ) {X_T}({G^ - }) (rather than X T ( F ) {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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