All Questions

Let $X$ be a Banach space and $K$ some compact Hausdorff space. I am interested in the dual space of the Banach space $$C(K; X) = \lbrace f: K \to X, \ f \text{ is continuous}\rbrace, \qquad \lVert ...

I would like to ask you for any good references regarding fractional order Sobolev spaces. I know Hitchhiker's guide to the fractional Sobolev spaces is a very popular one, and I found it to be quite ...

Let $$ X=\big\{\varphi\in\ell_\infty^{\,*}(\mathbb N) : \varphi(\{a_n\})=0\,\,\text{whenever $a_n\to 0$}\big\}. $$ If $\varphi_{\mathscr F}(\{a_n\})$ is the limit of $\{a_n\}$ with respect to the non-...

Working with the separable quotient problem for locally convex spaces we (with Saak Gabriyelyan) arrived to an interesting topology on the dual of a locally convex space and we would like to know if ...

Let $\mathbb{D} = \{ z \in \mathbb{C} : |z| < 1 \}$ be the unit disk. The Bergman space $A^1 = A^1(\mathbb{D})$ is the Banach space of holomorphic functions on $\mathbb{D}$ such that $$ \|f\|_{A^1} ...