Well-bounded and scalar-type spectral operators on spaces not containing 𝑐₀

Doust, Ian

doi:10.1090/S0002-9939-1989-0939963-X

Well-bounded and scalar-type spectral operators on spaces not containing $c_ 0$
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Proc. Amer. Math. Soc. 105 (1989), 367-370 Request permission

Abstract:

It is known that a necessary and sufficient condition for a well-bounded operator on a weakly complete complex Banach space to be scalar-type spectral is that its decomposition of the identity be of bounded variation. We show in this paper that this condition is necessary and sufficient exactly when the Banach space does not contain a subspace isomorphic to ${c_0}$.

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