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Apr
15
awarded  Custodian
Apr
15
comment Schauder basis for $c_0$
Well, the sequence $(e_k)_{k\in\mathbb N}$ is then a matrix.
Apr
15
reviewed Approve Show that the Euclidean algorithm works for Gaussian integers.
Apr
15
comment Schauder basis for $c_0$
Perhaps, the confusion comes from your somewhat unprecise writing $e_k=\delta_{j,k}$ which should be $e_k=(\delta_{j,k})_{j\in \mathbb N}$.
Mar
18
answered For any sequence from Frechet spaces there exists a sequence that takes it to zero
Mar
18
comment properties of a Köthe space s
What do you mean be $\log^\beta n$? Is it $(\log(n))^\beta$?
Mar
18
answered properties of a Köthe space s
Mar
18
comment Weak convergence + compactness = strong convergence?
A compact space does not a have a strictly weaker Hausdorff topology.
Mar
17
comment Characterization of product of dual dual Hilbert spaces.
Define $F_1(x_1)=F(x_1,0)$ and $F_2(x_2)=F(0,x_2)$.
Mar
12
answered Completion of a vector space inside a given Banach space
Feb
26
comment Suppose that $ T$ is a linear operator from a normed space $ X $ into normed space $ Y $.Prove that the following are equivalent
You could add iii: $T(K)$ is bounded for every compact subset of $X$. Since weakly compact sets are bounded, ii implies iii which gives i because you only have to prove that images of null sequences are bounded.
Feb
25
comment About the weak* closedness of the kernel of a continuous linear functional
Another idea is to use the real case and write $\varphi(x)= \Re \varphi(x) + i \Im \varphi(x) = \Re \varphi(x) - i \Re(i \varphi(x)) = \Re \varphi(x) - i \Re \varphi(ix)$
Feb
25
comment About the weak* closedness of the kernel of a continuous linear functional
One can split the proof into two parts: 1. A linear functional is continuous if (and, of course, only if) its kernel is closed. 2. The dual of $X^*$ endowed with the weak$*$ topology is $J(X)$. Both parts are true for complex Banach (and, more generally, locally convex) spaces.
Feb
20
comment Classes of measures that are closed under multiplication
@limanac The comment is no longer relevan and should be deleted.
Feb
20
revised Classes of measures that are closed under multiplication
New example.
Feb
20
comment Classes of measures that are closed under multiplication
Sorry for the wrong answer (which I deleted). Another try: If $\mathcal M_0$ is the space of all discrete measures then $\emptyset$ is the the only set so that each $\mu \in \mathcal M_0$ vanishes on it. Am I missing something?
Feb
19
answered A consequence of the open mapping theorem
Feb
19
comment A consequence of the open mapping theorem
You are right, I should have written this as an answer.
Feb
19
revised Classes of measures that are closed under multiplication
More details added.
Feb
19
comment A consequence of the open mapping theorem
Try $f:c_0 \to \mathbb R$, $(x_n)_{n\in\mathbb N} \mapsto \sum\limits_{n=1}^\infty x_n/2^n$.