Some Properties of Convex Sets Related to Fixed Points Theorems*.
Some properties of monotone type multivalued operators including accretive operators and the duality mapping are studied in connection with the structure of Banach spaces.
We investigate the stability of some properties of locally convex Riesz spaces in connection with subspaces and quotients and also the corresponding three-space-problems. We show that in the richer structure there are more positive answers than in the category of locally convex spaces.
For a closed subset I of the interval [0,1] we let A(I) = [v1(I),C(I)](1/2)2. We show that A(I) is isometric to a 1-complemented subspace of A(0,1), and that the Szlenk index of A(I) is larger than the Cantor index of I. We also investigate, for ordinals η < ω1, the bases structures of A(η), A*(η), and [the isometric predual of A(η)]. All the results of this paper extend, with obvious changes in the proofs, to the interpolation spaces .
We define the ε-product of an εb-space by quotient bornological spaces and we show that if G is a Schwartz εb-space and E|F is a quotient bornological space, then their εc-product Gεc(E|F) defined in [2] is isomorphic to the quotient bornological space (GεE)|(GεF).
We establish necessary and sufficient conditions under which weak Banach-Saks operators are weakly compact (respectively, L-weakly compact; respectively, M-weakly compact). As consequences, we give some interesting characterizations of order continuous norm (respectively, reflexive Banach lattice).