Geodesic
An operator satisfying Dunford's condition (C) but without bishop's property (β)
Glasgow mathematical journal, Tome 40 (1998) no. 3, pp. 427-430

Voir la notice de l'article provenant de la source Cambridge University Press

For X a complex Banach space and U an open subset of the complex plane С, let O (U, X) denote the space of analytic X- valued functions defined on U. This is a Frechet space when endowed with the topology of uniform convergence on compact subsets, and the space X may be viewed as simply the constants in O(U, X). Every bounded operator T on X induces a continuous mapping TU on O(U, X) given by (Tuf)(λ) = (λ – T)f(λ) for every f e O(U, X) and λ e U. Corresponding to each closed F ⊂ С there is also an associated analytic subspace XT(F) = X ∩ ran(7c//F). For an arbitrary T e L(X), the spaces XT(F) are T-invariant, generally non-closed linear manifolds in X. 
Miller, T. L.; Miller, V. G. An operator satisfying Dunford's condition (C) but without bishop's property (β). Glasgow mathematical journal, Tome 40 (1998) no. 3, pp. 427-430. doi: 10.1017/S0017089500032754
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