A Note on Equivalent Extended Bases.
A note on extensions of Pełczyński's decomposition method in Banach spaces
Let X,Y,A and B be Banach spaces such that X is isomorphic to Y ⊕ A and Y is isomorphic to X ⊕ B. In 1996, W. T. Gowers solved the Schroeder-Bernstein problem for Banach spaces by showing that X is not necessarily isomorphic to Y. In the present paper, we give a necessary and sufficient condition on sextuples (p,q,r,s,u,v) in ℕ with p + q ≥ 2, r + s ≥ 1 and u, v ∈ ℕ* for X to be isomorphic to Y whenever these spaces satisfy the following decomposition scheme: ⎧ , ⎨ ⎩ . Namely, Ω = (p-u)(s-r-v)...
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.