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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