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awarded  elementary-set-theory
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awarded  Nice Answer
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Feb
15
comment weak sequential continuity of linear operators
@Svetoslav: Unboundedness of T implies that for each $M>0$ there exists x with norm 1 such that $\|Tx\|>M$. Thus for each positive integer n take $y_n$ with norm 1 such that $\|Ty_n\|>n^2$, and take $x_n=\frac1n y_n$.
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awarded  Enlightened
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15
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31
comment Example of operator with spectrum equal to $\mathbb{C}$?
You have examples for 2 & 3? If so, could you take a direct sum of those?
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30
awarded  Necromancer
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28
awarded  Nice Answer
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awarded  Guru
Jan
23
comment Why does the Gram-Schmidt procedure divide by 0 on a linearly dependent lists of vectors?
@ihadanny: It is 0 because it is a vector in the span of the $e_i$s whose inner product with each $e_i$ is 0.
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22
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Jan
3
reviewed Close why don't standard analysis texts relax the injectivity requirement of the multivariable change of variables theorem?
Jan
3
comment $\lim_{x\to c} f(x)=l \implies f(x)$ is defined in a neighbourhood $c$?
It depends on context not given. Sometimes yes it would imply that by the definition.
Jan
3
reviewed Close $\left (1+\frac{a}{b} \right) \left(1+\frac{b}{c} \right) \left(1+\frac{c}{a} \right) \geq 2 \left ( 1+\frac{a+b+c}{\sqrt[3]{abc}} \right).$