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For suitable Banach spaces X and Y with Schauder decompositions and a suitable closed subspace M of some COMPACT operator space from X to Y, it is shown that the strong Banach-Saks-ness of all evaluation operators on M is a sufficient condition for the weak Banach-Saks PROPERTY of M, where for each xÎX and y*ÎY*, the evaluation operators on M are defined by fx (T)= Tx and yy* (T)= T*y*.

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In this paper, we present a study of RELATIVELY connected sublocales. Connected sublocales are RELATIVELY connected, not conversely. We study conditions under which RELATIVELY connected sublocales are connected. The development of this study is subsequently utilized to characterize what we call C-normal frames. We show that normal frames are C-normal but not conversely. Some results concerning J-frames are presented; amongst other things, we prove that regular continuous frames are rim-COMPACT. A rim-COMPACT J-frame is regular continuous. The latter is used to show that the least COMPACTification of a regular continuous J-frame coincides with its Freudenthal COMPACTification. In turn, this contributes to the known conditions under which the least COMPACTification is perfect.

The general RELATIVELY isotropic mean Landsberg metrics contain the general RELATIVELY isotropic Landsberg metrics. A class of Finsler metrics is given, in which the mentioned two concepts are equivalent. In this paper, an interpretation of general RELATIVELY isotropic mean Landsberg metrics is found by using C-conformal transformations. Some necessary conditions for a general RELATIVELY isotropic mean Landsberg metric, as well as generalized Landsberg metric to be a Riemannian metric are also found.