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6:58 AM
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Q: A difficulty in understanding a paragraph in Israel Gohberg.

IntuitionHere is the paragraph that is not clear for me: Could anyone explain it for me please?

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Q: A difficulty in understanding a second paragraph in Israel Gohberg.

IntuitionThe paragraph is given in the following pictures: If $A$ is an operator from $H_{1}$ to $H_{2}$, The paragraph is divided into 5 sentences. I could not understand the first, second, forth and fifth sentences. Could anyone explain them for me please? Thanks!

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Q: A conjecture about filters

portonLet $\mathfrak{F}(S)$ denotes the set of filters (including the improper filter) on a poset $S$, ordered reversely to set theoretic inclusion of filters. Let $Da$ for a lattice element $a$ denote its sublattice $\{ x \mid x \leq a \}$. Let $Z(X)$ denotes the set of complemented elements of the la...

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Q: Finding the image of an operator.

IntuitionLet $T:l_{2} \rightarrow l_{2}$ be defined by $$T(x) = \left(x_{1},\frac{x_{2}}{2},\frac{x_{3}}{4},\ldots,\frac{x_{n}}{2^{n-1}},\ldots \right)$$ where $x = (x_{1},x_{2},.....).$ Find Im$T$. I know that the kernel of this operator is $\{0\}$ and I know that the sum of the dim Im$T$ + dim ker$...

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Q: Finding the image of another operator.

IdonotknowLet $n \in \mathbb{N^{*}}$ and define $T_{n}:l_{2} \rightarrow l_{2}$ by $$T_{n}(x) = (\frac{x_{n}}{n},\frac{x_{n + 1}}{n + 1},... ).$$ where $x = (x_{1},x_{2},.....).$ Then,$$T_{n}^{*}(x) = (0,...,0,\frac{x_{1}}{n},\frac{x_{2}}{n + 1},... ).$$ Where the zeros in the adjoint are $n-1$ times. ...

Two of them were created by Intuition.
 
 
4 hours later…
10:50 AM
I've edited the two questions with the tag "image-of-operator", and essentially have killed the tag.
 
@JohnMa Did you mean some other tag? I still see it here:
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Q: Finding the image of another operator.

IdonotknowLet $n \in \mathbb{N^{*}}$ and define $T_{n}:l_{2} \rightarrow l_{2}$ by $$T_{n}(x) = (\frac{x_{n}}{n},\frac{x_{n + 1}}{n + 1},... ).$$ where $x = (x_{1},x_{2},.....).$ Then,$$T_{n}^{*}(x) = (0,...,0,\frac{x_{1}}{n},\frac{x_{2}}{n + 1},... ).$$ Where the zeros in the adjoint are $n-1$ times. ...

 
11:09 AM
oops, I mean "invertible-operators"
Um, the way the users "intuition" and "Idonotknow" ask their questions, I assume they are held by the same person. Their recent questions should be tagged "functional analysis" instead of the a little bit more advanced "operator theory".
 

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