Relation between fixed point and asymptotical center of nonexpansive maps.
In this paper we get some relations between the boundary point spectrum of the generator A of a C0-semigroup and the generator A* of the dual semigroup. This relations combined with the results due to Lyubich-Phong and Arendt-Batty, yield stability results on positive C0-semigroups.
We characterize the class of weights, invariant under dilations, for which a modified fractional integral operator maps weak weighted Orlicz spaces into appropriate weighted versions of the spaces , where . This generalizes known results about boundedness of from weak into Lipschitz spaces for and from weak into . It turns out that the class of weights corresponding to acting on weak for of lower type equal or greater than , is the same as the one solving the problem for weak...
A linear operator T: D(T) ⊂ X → Y, when X and Y are normed spaces, is called ubiquitously open (UO) if every infinite dimensional subspace M of D(T) contains another such subspace N for which T|N is open (in the relative sense). The following properties are shown to be equivalent: (i) T is UO, (ii) T is ubiquitously almost open, (iii) no infinite dimensional restriction of T is injective and precompact, (iv) either T is upper semi-Fredholm or T has finite dimensional range, (v) for each infinite...