JournalszaaVol. 13, No. 3pp. 377–385

LφL_{\varphi}-Spaces and some Related Sequence Spaces

  • Johann Boos

    Fernuniversität-GHS, Hagen, Germany
  • Karl-Goswin Grosse-Erdmann

    Fernuniversität-GHS, Hagen, Germany
  • T. Leiger

    Tartu University, Estonia
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In view of closed graph theorems in case of maps defined by operator-valued matrices LφL_{\varphi}-spaces were recently introduced by two of the present authors as a generalization of separable FK(X)FK(X)-spaces. In this paper we study the class of LφL_{\varphi}-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 LφL_{\varphi}-spaces as range spaces, and paralleling a result of Qiu we prove that the class of LφL_{\varphi}-spaces is the best-possible choice here. As a consequence we show that for any LφL_{\varphi}-space EE every matrix domain EAE_A is again an LφL_{\varphi}-space.

Cite this article

Johann Boos, Karl-Goswin Grosse-Erdmann, T. Leiger, LφL_{\varphi}-Spaces and some Related Sequence Spaces. Z. Anal. Anwend. 13 (1994), no. 3, pp. 377–385

DOI 10.4171/ZAA/507