Emre TaştünerDepartment of Mathematics, Middle East Technical University, 06800 Ankara, Turkey

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Murat Hayrettin YurdakulDepartment of Mathematics, Middle East Technical University, 06800 Ankara, Turkey

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Let E, G be Fréchet spaces and F be a complete locally convex space. It is observed that the existence of a continuous linear not almost bounded operator T on E into F factoring through G causes the existence of a common nuclear Köthe subspace of the triple (E, G, F). If, in addition, F has the property (y), then (E, G, F) has a common nuclear Köthe quotient.

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