User Jochen

16 votes

Accepted

Finite dimensional subspace of $C([0,1])$

answered Mar 26, 2014 at 7:53

13 votes

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Prove the set of sequences $c_0$ which converge to zero in $l_{\infty}$ is closed.

answered Mar 11, 2014 at 14:11

12 votes

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If $f(x) + f'(x) + f''(x) \to A$ as $x \to \infty$, then show that $f(x) \to A$ as $x \to \infty$

answered Mar 25, 2014 at 12:39

12 votes

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Question about sum of l'p spaces

answered Aug 31, 2013 at 19:55

12 votes

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Density of test functions in the space of distributions -- a clarification

answered Mar 19, 2019 at 8:28

12 votes

Can we prove the chain rule without using an artificial trick?

answered Nov 20, 2022 at 7:49

11 votes

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If $M=M^{\perp\perp}$ for every closed subspace $M$ of a pre-Hilbert space then $H$ is complete

answered Jan 18, 2022 at 10:31

11 votes

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If $T: X \to Y$ is norm-norm continuous then it is weak-weak continuous

answered Aug 19, 2014 at 8:03

10 votes

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Convergence in distrubution sense and convergence of distribution to a distrubution.

answered Mar 10, 2019 at 9:51

9 votes

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Topologies of test functions and distributions

answered Mar 10, 2014 at 8:17

8 votes

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Extension of character in Banach algebras

answered Apr 24, 2014 at 7:05

8 votes

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if number of extreme points of $B_X$ is finite, then $X$ is of finite dimensional?

answered Jul 14, 2018 at 7:14

7 votes

Is $X^$ complete with weak-topology

answered Jul 19, 2016 at 6:44

7 votes

A relative compactness criterion in $\ell^p$

answered Sep 17, 2013 at 8:47

7 votes

Accepted

Prove or disprove : If $E[Y|X]=X$, $E[X|Y]=Y$, and both $E[X^2]\mbox{ and }E[Y^2]$ are finite, then $P[X=Y]=1$.

answered Aug 26, 2013 at 7:35

6 votes

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Do sequences fully specify the topology of $\mathcal{D}(\Omega)$ and $\mathcal{D}'(\Omega)$?

answered Feb 6, 2015 at 8:15

6 votes

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Are $C^k[0,1]$, with the $C^k$ norm, distinct as Banach spaces?

answered Jan 19, 2016 at 12:27

6 votes

Definition of Sobolev space via distribution

answered Mar 15, 2017 at 14:55

6 votes

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Counter-example for closed mapping theorem in normed spaces

answered Feb 28, 2018 at 13:59

6 votes

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What is the (strong) dual of a projective/inductive limit?

answered Sep 27, 2018 at 8:24

6 votes

Is "assignment" a canonical term in math?

answered Jul 9, 2019 at 7:26

5 votes

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Krein-Milman theorem and dividing pizza with toppings

answered May 24, 2017 at 7:06

5 votes

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Weak$*$ topology is metrizable iff $X$ is finite dimensional.

answered Oct 24, 2017 at 6:44

5 votes

Accepted

If the image of an orthonormal basis is bounded, is the linear operator also bounded?

answered Oct 10, 2017 at 12:41

5 votes

Accepted

Continuous semi-norms on subspace

answered Jul 18, 2016 at 11:12

5 votes

Example of a topological vector space which is not locally convex

answered Jan 5, 2016 at 16:17

5 votes

Sequential continuity implies continuity in the weak topology on a normed space

answered Mar 10, 2016 at 7:31

5 votes

Accepted

Show that the Open Mapping Theorem requires both spaces to be complete

answered Dec 10, 2014 at 7:33

5 votes

Accepted

Continuity of a stochastic process

answered Sep 3, 2015 at 10:20

5 votes

How many surjections are there from a set of 3 elements onto a set of 2 elements?

answered Aug 29, 2012 at 10:23

Stack Exchange Network

389 Answers

Finite dimensional subspace of $C([0,1])$

Prove the set of sequences $c_0$ which converge to zero in $l_{\infty}$ is closed.

If $f(x) + f'(x) + f''(x) \to A$ as $x \to \infty$, then show that $f(x) \to A$ as $x \to \infty$

Question about sum of l'p spaces

Density of test functions in the space of distributions -- a clarification

Can we prove the chain rule without using an artificial trick?

If $M=M^{\perp\perp}$ for every closed subspace $M$ of a pre-Hilbert space then $H$ is complete

If $T: X \to Y$ is norm-norm continuous then it is weak-weak continuous

Convergence in distrubution sense and convergence of distribution to a distrubution.

Topologies of test functions and distributions

Extension of character in Banach algebras

if number of extreme points of $B_X$ is finite, then $X$ is of finite dimensional?

Is $X^$ complete with weak-topology

A relative compactness criterion in $\ell^p$

Prove or disprove : If $E[Y|X]=X$, $E[X|Y]=Y$, and both $E[X^2]\mbox{ and }E[Y^2]$ are finite, then $P[X=Y]=1$.

Do sequences fully specify the topology of $\mathcal{D}(\Omega)$ and $\mathcal{D}'(\Omega)$?

Are $C^k[0,1]$, with the $C^k$ norm, distinct as Banach spaces?

Definition of Sobolev space via distribution

Counter-example for closed mapping theorem in normed spaces

What is the (strong) dual of a projective/inductive limit?

Is "assignment" a canonical term in math?

Krein-Milman theorem and dividing pizza with toppings

Weak$*$ topology is metrizable iff $X$ is finite dimensional.

If the image of an orthonormal basis is bounded, is the linear operator also bounded?

Continuous semi-norms on subspace

Example of a topological vector space which is not locally convex

Sequential continuity implies continuity in the weak topology on a normed space

Show that the Open Mapping Theorem requires both spaces to be complete

Continuity of a stochastic process

How many surjections are there from a set of 3 elements onto a set of 2 elements?