Question

Is a continuous linear injective map between Hilbert spaces with dense image invertible?

score 250 · Answer 1 · 2022-06-02 15:57:23

250

Views

Is a continuous linear injective map between Hilbert spaces with dense image invertible?

Published on 02 Jun 2022 - 15:57

score 46 · Answer 2 · 2026-03-26 14:34:20

46

Views

There is a linear extension $\hat \ell: X \to \mathbb R$ of $\ell$ such that $\hat \ell \le m$ on $A$.

Published on 26 Mar 2026 - 14:34

score 92 · Answer 3 · 2026-03-27 01:47:35

92

Views

Let $A$ and $B$ be nonempty disjoint closed sets such that $A$ is compact. There exists a neighborhood $V$ of $0$ such that $(A+V) \cap B=\emptyset$

Published on 27 Mar 2026 - 1:47

score 59 · Answer 4 · 2022-06-08 09:37:57

59

Views

Let $A$ be a convex. Is it true that $\operatorname{aint} (A) \neq \emptyset \implies \operatorname{aint} (A) = \operatorname{int} (A)$?

Published on 08 Jun 2022 - 9:37

score 40 · Answer 5 · 2022-06-08 12:37:02

40

Views

What is the definition of: A filter on $A$ converges to a point of $E$?

Published on 08 Jun 2022 - 12:37

score 27 · Answer 6 · 2022-06-08 13:48:14

27

Views

About barrelled subspace.

Published on 08 Jun 2022 - 13:48

score 81 · Answer 7 · 2022-06-08 20:22:48

81

Views

$A$ and $B$ precompact , closed and disjoint subset of $E$.

Published on 08 Jun 2022 - 20:22

score 49 · Answer 8 · 2022-06-09 18:32:43

49

Views

Continuous function between topological vector spaces

Published on 09 Jun 2022 - 18:32

score 1.7k · Answer 9 · 2026-03-27 16:26:18

1.7k

Views

On the definition of weak and weak-* topologies

Published on 27 Mar 2026 - 16:26

score 189 · Answer 10 · 2022-06-11 09:13:39

189

Views

Let $A:=\{x_1, \ldots, x_{n+1}\}$ be an affinely independent. Then $\operatorname{int} (\operatorname{conv} A) \neq \emptyset$

Published on 11 Jun 2022 - 9:13

score 27 · Answer 11 · 2022-06-12 07:28:31

27

Views

Does this theorem about algebraic/topological interiors hold in case $X$ is non-Hausdorff?

Published on 12 Jun 2022 - 7:28

score 84 · Answer 12 · 2022-06-12 07:58:10

84

Views

Let $f_1, f_2 \in E^*$ such that $\{f_1, f_2\}$ is linearly independent. Is the map $x \mapsto (f_1(x), f_2(x))$ injective or surjective?

Published on 12 Jun 2022 - 7:58

score 249 · Answer 13 · 2026-03-26 09:37:16

249

Views

Discrete-time dynamical systems with variable state space dimensions (or output space dimensions)

Published on 26 Mar 2026 - 9:37

score 62 · Answer 14 · 2022-06-14 22:44:34

62

Views

$c_{00}$ is closed?

Published on 14 Jun 2022 - 22:44

score 68 · Answer 15 · 2022-06-16 13:08:05

68

Views

Topologies agree on infinite-dimensional simplex

Published on 16 Jun 2022 - 13:08

List Question

Is a continuous linear injective map between Hilbert spaces with dense image invertible?

There is a linear extension $\hat \ell: X \to \mathbb R$ of $\ell$ such that $\hat \ell \le m$ on $A$.

Let $A$ and $B$ be nonempty disjoint closed sets such that $A$ is compact. There exists a neighborhood $V$ of $0$ such that $(A+V) \cap B=\emptyset$

Let $A$ be a convex. Is it true that $\operatorname{aint} (A) \neq \emptyset \implies \operatorname{aint} (A) = \operatorname{int} (A)$?

What is the definition of: A filter on $A$ converges to a point of $E$?

About barrelled subspace.

$A$ and $B$ precompact , closed and disjoint subset of $E$.

Continuous function between topological vector spaces

On the definition of weak and weak-* topologies

Let $A:=\{x_1, \ldots, x_{n+1}\}$ be an affinely independent. Then $\operatorname{int} (\operatorname{conv} A) \neq \emptyset$

Does this theorem about algebraic/topological interiors hold in case $X$ is non-Hausdorff?

Let $f_1, f_2 \in E^*$ such that $\{f_1, f_2\}$ is linearly independent. Is the map $x \mapsto (f_1(x), f_2(x))$ injective or surjective?

Discrete-time dynamical systems with variable state space dimensions (or output space dimensions)

$c_{00}$ is closed?

Topologies agree on infinite-dimensional simplex

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