In view of closed graph theorems in case of maps defined by operator-valued matrices -spaces were recently introduced by two of the present authors as a generalization of separable -spaces. In this paper we study the class of -spaces and a few closely related classes of sequence spaces. It is shown that an analogue of Kalton’s closed graph theorem holds for matrix mappings if we consider -spaces as range spaces, and paralleling a result of Qiu we prove that the class of -spaces is the best-possible choice here. As a consequence we show that for any -space every matrix domain is again an -space.
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Johann Boos, Karl-Goswin Grosse-Erdmann, T. Leiger, -Spaces and some Related Sequence Spaces. Z. Anal. Anwend. 13 (1994), no. 3, pp. 377–385DOI 10.4171/ZAA/507