Some subadditivity inequalities for matrices and concave functions also hold for Hilbert space operators, but (unfortunately!) with an additional $\varepsilon $ term. It does not seem possible to erase this residual term. However, in case of compact operators we show that the $\varepsilon $ term is unnecessary. Further, these inequalities are strict in a certain sense when some natural assumptions are satisfied. The discussion also emphasizes matrices and their compressions and several open questions or conjectures are considered, both in the matrix and operator settings.

Drepanophycus spinaeformis Göppert is a long ranging Devonian plant. Although reported from numerous localities, it is far from well understood. Observations on specimens from the Emsian Strathmore Group of Scotland have revealed variation in forms of branching including root-like axes on branches interpreted as rhizomes. The anatomy of the xylem is described from uncompressed pyrite permineralisations. Cuticle characteristics are also described and discussed. The systematic position of the plant is debated since, although the morphology of the leaves, leaf traces, roots and xylem indicate an affinity with the lycopods, there is some doubt as to whether sporangial position permits inclusion in this group.