Let $(E_{i})_{i\in I}$ be a family of normed spaces and $\lambda $ a space of scalar generalized sequences. The $\lambda $-sum of the family $(E_{i})_{i\in I}$ of spaces is \[ \lambda \lbrace (E_{i})_{i\in I}\rbrace :=\lbrace (x_{i})_{i\in I},x_{i}\in E_{i}, \quad \text{and}\quad (\Vert x_{i}\Vert )_{i\in I}\in \lambda \rbrace}. \] Starting from the topology on $\lambda $ and the norm topology on each $E_i,$ a natural topology on $\lambda \lbrace (E_i)_{i\in I}\rbrace $ can be defined. We give conditions for $\lambda \lbrace (E_i)_{i\in I}\rbrace $ to be quasi-barrelled, barrelled or locally complete.
In search for new forestation tree species for future Central European climate conditions, Mediterranean evergreen oak taxa are investigated for their summer drought- and winter frost-hardiness. Here we report on the winter performance of the photosynthetic apparatus of Quercus × hispanica Lam. and its evergreen parental species Q. suber L. under extraordinary harsh winter conditions. Both taxa showed a strong decline of photosystem II (PSII) quantum efficiency (Fv/Fm) with a concomitant increase in the deepoxidation state (DES) of the xanthophyll pigments depending on (severe) frost events during winter, and these parameters significantly correlated with minimum air temperatures during periods of chronic photoinhibition at mid-winter, but not at the onset of winter in response to the first frost nights. Fv/Fm and DES correlated with each other in both taxa throughout the winter. and V. Holland, W. Brüggemann.