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 Yearling
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  • 15 votes cast
Apr
12
asked Decomposing continuous linear functionals on a locally convex space with 2 seminorms
Mar
19
awarded  Yearling
Mar
4
asked Weak convergence and norm convergnce along a subsequnece in $H^1(\Omega)$
Feb
15
accepted What is the Fourier transform of $e^{(-a+bi)x^2}$?
Feb
13
asked What is the Fourier transform of $e^{(-a+bi)x^2}$?
Dec
7
accepted Summable family in a normed linear space
Dec
7
revised Summable family in a normed linear space
added 2 characters in body
Dec
7
asked Summable family in a normed linear space
Dec
7
accepted What are all the group endomorphisms of the circle group?
Dec
3
awarded  Curious
Dec
2
asked What are all the group endomorphisms of the circle group?
Jan
1
comment Does countable intersection of linear subspaces with finite codimensions have countable codimension?
Thanks for your example.
Jan
1
answered The weak$^*$ topology on $X^*$ is not first countable if $X$ has uncountable dimension.
Jan
1
comment The weak$^*$ topology on $X^*$ is not first countable if $X$ has uncountable dimension.
Thank you very much. I think the last comment by @DavidMitra is the answer. Do you want to write up the answer? Or should I answer my own question?
Jan
1
comment The weak$^*$ topology on $X^*$ is not first countable if $X$ has uncountable dimension.
But Uniform Boundedness Theorem requires the normed space in question to be complete, right?
Jan
1
comment The weak$^*$ topology on $X^*$ is not first countable if $X$ has uncountable dimension.
Thank you. But why are weak* convergent sequences norm-bounded?
Dec
31
comment The weak$^*$ topology on $X^*$ is not first countable if $X$ has uncountable dimension.
You mean this sequence in $X^*$? I see where this is going. The sequence is w*-bounded, but not norm-bounded. This is not quite a contradiction because w*-boundedness and norm-boundedness are not quite the same.
Dec
31
asked The weak$^*$ topology on $X^*$ is not first countable if $X$ has uncountable dimension.
Dec
31
answered Does countable intersection of linear subspaces with finite codimensions have countable codimension?
Dec
31
awarded  Commentator