A note on extremality and completeness in financial markets with infinitely many risky assets
A Note on Extreme and Exposed Points in Cn(I).
A note on extreme contractions on -spaces
A Note on Extreme Positive Definite Matrices.
A note on Fiedler-Moravek combinatorial problem
A note on finite codimensional linear isometries of into .
A note on fractional integration
A note on Fréchet-Urysohn locally convex spaces.
Recently Cascales, Kąkol and Saxon showed that in a large class of locally convex spaces (so called class G) every Fréchet-Urysohn space is metrizable. Since there exist (under Martin’s axiom) nonmetrizable separable Fréchet-Urysohn spaces Cp(X) and only metrizable spaces Cp(X) belong to class G, we study another sufficient conditions for Fréchet-Urysohn locally convex spaces to be metrizable.
A Note on Free Quantum Groups
We study the free complexification operation for compact quantum groups, . We prove that, with suitable definitions, this induces a one-to-one correspondence between free orthogonal quantum groups of infinite level, and free unitary quantum groups satisfying .
A note on fusion Banach frames
For a fusion Banach frame for a Banach space , if is a fusion Banach frame for , then is called a fusion bi-Banach frame for . It is proved that if has an atomic decomposition, then also has a fusion bi-Banach frame. Also, a sufficient condition for the existence of a fusion bi-Banach frame is given. Finally, a characterization of fusion bi-Banach frames is given.
A note on -spaces.
A note on Gehring's lemma.
A note on geometric characterization of Fréchet differentiability
A note on global implicit function theorem.
A note on implicit functions in locally convex spaces.
A Note on Inductive Limits of Linear Spaces.
A note on infinite dimensional convex sets.
A note on integral inequalities and embeddings of Besov spaces.
A note on intermediate differentiability of Lipschitz functions
Let be a Lipschitz function on a superreflexive Banach space . We prove that then the set of points of at which has no intermediate derivative is not only a first category set (which was proved by M. Fabian and D. Preiss for much more general spaces ), but it is even -porous in a rather strong sense. In fact, we prove the result even for a stronger notion of uniform intermediate derivative which was defined by J.R. Giles and S. Sciffer.
A note on interpolation and higher integrability.