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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Equivalent conditions for decomposable operators

Author: Ridgley Lange
Journal: Proc. Amer. Math. Soc. 82 (1981), 401-406
MSC: Primary 47B40
MathSciNet review: 612729
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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 Frunza'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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Keywords: Decomposable operator, spectral maximal space
Article copyright: © Copyright 1981 American Mathematical Society