On a class of Banach spaces of analytic functions.
It is proved that if a Kothe sequence space is monotone complete and has the weakly convergent sequence coefficient WCS, then is order continuous. It is shown that a weakly sequentially complete Kothe sequence space is compactly locally uniformly rotund if and only if the norm in is equi-absolutely continuous. The dual of the product space of a sequence of Banach spaces , which is built by using an Orlicz function satisfying the -condition, is computed isometrically (i.e. the exact...
We consider scalar products on a given Hilbert space parametrized by bounded positive and invertible operators defined on this space, and orthogonal projectors onto a fixed closed subspace of the initial Hilbert space corresponding to these scalar products. We show that the projector is an analytic function of the scalar product, we give the explicit formula for its Taylor expansion, and we prove some algebraic formulas for projectors.