Extension of group-valued set functions defined on lattices
Extension of measure-like set functions
Extension of vector measures
Extension theorems (vector measures on quantum logics)
Extensions of additive mappings
Extensions of measurable functions
Extensions of positive operators and extreme points. I
Extensions of positive operators and extreme points. II
Extensions of positive operators and extreme points. III
Extensions of positive operators and extreme points. IV
Extensions of semigroup valued, finitely additive measures.
Extremal preimage measures and measurable weak sections
Factorization through Hilbert space and the dilation of L(X,Y)-valued measures
We present a general necessary and sufficient algebraic condition for the spectral dilation of a finitely additive L(X,Y)-valued measure of finite semivariation when X and Y are Banach spaces. Using our condition we derive the main results of Rosenberg, Makagon and Salehi, and Miamee without the assumption that X and/or Y are Hilbert spaces. In addition we relate the dilation problem to the problem of factoring a family of operators through a single Hilbert space.
Fields with analytic structure
First class selectors for weakly upper semi-continuous multi-valued maps in Banach spaces.
Fréchet-spaces-valued measures and the AL-property.
Associated with every vector measure m taking its values in a Fréchet space X is the space L1(m) of all m-integrable functions. It turns out that L1(m) is always a Fréchet lattice. We show that possession of the AL-property for the lattice L1(m) has some remarkable consequences for both the underlying Fréchet space X and the integration operator f → ∫ f dm.
Fredholm random operators and random subspaces in Banach spaces
From weak to strong types of -convergence by the Bocce criterion
Necessary and sufficient oscillation conditions are given for a weakly convergent sequence (resp. relatively weakly compact set) in the Bochner-Lebesgue space to be norm convergent (resp. relatively norm compact), thus extending the known results for . Similarly, necessary and sufficient oscillation conditions are given to pass from weak to limited (and also to Pettis-norm) convergence in . It is shown that tightness is a necessary and sufficient condition to pass from limited to strong convergence....
Fubini theorems for bornological measures
Funktionalanalytische Fassung des Satzes von Radon-Nikodym. I.