THE CLOSED RANGE PROPERTY FOR BANACH SPACE OPERATORS

MILLER, THOMAS L. ; MÜLLER, VLADIMIR

Glasgow mathematical journal, Tome 50 (2008) no. 1, pp. 17-26

Résumé

Let T be a bounded operator on a complex Banach space X. Let V be an open subset of the complex plane. We give a condition sufficient for the mapping f(z)↦ (T−z)f(z) to have closed range in the Fréchet space H(V, X) of analytic X-valued functions on V. Moreover, we show that there is a largest open set U for which the map f(z)↦ (T−z)f(z) has closed range in H(V, X) for all V⊆U. Finally, we establish analogous results in the setting of the weak–* topology on H(V, X*).

Détail

DOI : 10.1017/S0017089507003898

Mots-clés : 47A11

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