Jochen Wengenroth
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 4h comment embeds in $L(c_{0},\ell_{1})$ By Pitt's theorem $L(c_0,\ell^1)=K(c_0,\ell^1)=\ell^1 \tilde{\otimes}_\varepsilon \ell^1$. There is an article of Bombal, Fernandez-Unzueta, and Villanueva Local structure and copies of $c_0$ and $\ell^1$ in the tensor product of Banach spaces but, unfortunately, their main result theorem 2.1 apparently does not apply here. 6h revised embeds in $L(c_{0},\ell_{1})$ improved formatting 9h comment Upper bound on the norm of the inverse of matrices with zero limit The example shows that there is no hope to bound the norm of an inverse in terms of the norm of a matrix. 1d comment Upper bound on the norm of the inverse of matrices with zero limit Calculate the norm of $\begin{bmatrix} 1 & 0\\ 0 & \varepsilon\end{bmatrix}$ and its inverse to see that there is no hope. Apr 29 comment Are compactly supported continuous functions dense in the Continuous functions of Sobolev space? Waht do you mean by $C_c(\overline{\Omega})$? Continuous functions on $\mathbb R^d$ such that the support is a compact subset of $\overline{\Omega}$? For "nice" $\Omega$ this would be the space of continuous functions on $\Omega$ vanishing at the boundary. Apr 29 comment approximating smooth functions by non-smooth ones, in the distribution topology The "usual" topology on $\mathscr D'$ is convergence of $u_n(\varphi)\to u(\varphi)$ FOR ALL $\varphi \in \mathscr D$ (this describes the weak$^*$ topology). For $\varphi \in \mathscr D$ the derivatives $\varphi^{(k)}$ again belong to $\mathscr D$, hence $u_n^{(k)}(\varphi)=(-1)^k u_n(\varphi^{(k)}) \to (-1)^{k}u(\varphi^{(k)})=u^{(k)}(\varphi)$. Apr 29 comment approximating smooth functions by non-smooth ones, in the distribution topology As stated, this is a strange question. Perhaps you can give some more background. Note that convergence $u_n\to u$ in $\mathscr D'$ automatically implies $u_n^{(k)} \to u^{(k)}$ in $\mathscr D'$ for all $k\in\mathbb N$. This is a trivial but important fact in distribution theory. Apr 29 answered Can the topological algebra of analytic functions be endowed with a norm that defines the natural topology? Apr 25 revised Attempted Banachification of a space Improved conjecture. Apr 25 awarded Nice Answer Apr 25 revised Attempted Banachification of a space Corrected spelling. Apr 25 comment Attempted Banachification of a space In terms of Banach discs the question whether a space has a finer Banach topology has a trivial answer: This is so if and only if there is an absorbing Banach disc. Apr 25 comment Attempted Banachification of a space Such bounded sets $B$ are called Banach discs and the inductive limit topology you mention is the associated ultrabornological topology. Apr 24 revised Attempted Banachification of a space added 708 characters in body Apr 24 answered Attempted Banachification of a space Apr 12 revised Extension of functions from geodesically convex compact sets in a Riemannian manifold Typo corrected ($\rho$ instead of $r$) Apr 5 comment Is this continuous linear map weakly compact? I think you should say precisely what you mean by a weakly compact holomorphic mapping and by a weakly compact operator between locally convex spaces. Mar 29 answered Holomorphy of a function with values in a Hilbert space Mar 17 comment Structure of chain of duals in functional analysis Note that $X$ and $X^{**}$ can be isomorphic although $X$ is not reflexive. Mar 11 awarded Nice Question