Question

Prove the inverse map of an injective linear function with closed graph from $U$ to $V$ (Banach spaces) is continuous iff the image is closed in $V$.

score 283 · Answer 1 · 2020-11-17 02:15:07

283

Views

Prove the inverse map of an injective linear function with closed graph from $U$ to $V$ (Banach spaces) is continuous iff the image is closed in $V$.

Published on 17 Nov 2020 - 2:15

score 143 · Answer 2 · 2020-12-05 04:30:56

143

Views

Counterexample of closed graph theorem when the image space is Hausdorff space but not compact?

Published on 05 Dec 2020 - 4:30

score 61 · Answer 3 · 2020-12-09 22:07:02

61

Views

Why is the derivative Operator defined over $C^2([-1,1])$ not closed?

Published on 09 Dec 2020 - 22:07

score 160 · Answer 4 · 2020-12-18 19:20:23

160

Views

A question about Banach spaces and closed graph theory

Published on 18 Dec 2020 - 19:20

score 330 · Answer 5 · 2020-12-20 17:25:44

330

Views

$C^1[0,1]$ is not banach using the closed graph theory

Published on 20 Dec 2020 - 17:25

score 377 · Answer 6 · 2021-01-24 05:37:58

377

Views

Proof of that the graph of subdifferential is closed when $f$ is closed proper convex function on $\mathbb{R}^n$.

Published on 24 Jan 2021 - 5:37

score 32 · Answer 7 · 2021-02-16 05:03:44

32

Views

How to determine mathematically that an expression with one independent variable forms a closed area or not

Published on 16 Feb 2021 - 5:03

score 812 · Answer 8 · 2021-03-09 09:25:02

812

Views

A linear operator $T$ is closed if and only if whenever $x_n\rightarrow x$ and $Tx_n\rightarrow y$, $y=Tx$.

Published on 09 Mar 2021 - 9:25

score 366 · Answer 9 · 2021-04-15 13:55:28

366

Views

Closed graph theorem for metric spaces

Published on 15 Apr 2021 - 13:55

score 291 · Answer 10 · 2021-04-29 20:13:12

291

Views

Application of Closed Graph Theorem for l2 space

Published on 29 Apr 2021 - 20:13

score 135 · Answer 11 · 2021-07-06 01:15:02

135

Views

Show that graphs of a contraction map and its inverse are both closed.

Published on 06 Jul 2021 - 1:15

score 189 · Answer 12 · 2021-09-08 13:31:21

189

Views

Question 2.18 from Brezis: Would someone help me to understand a solution given to this question?

Published on 08 Sep 2021 - 13:31

score 105 · Answer 13 · 2021-09-18 07:45:23

105

Views

On closed-graph theorem

Published on 18 Sep 2021 - 7:45

score 185 · Answer 14 · 2021-11-26 04:59:18

185

Views

How can I prove that this Linear operator is closed?

Published on 26 Nov 2021 - 4:59

score 136 · Answer 15 · 2021-12-06 17:41:23

136

Views

Accumulation point of a discrete Spectrum

Published on 06 Dec 2021 - 17:41

List Question

Prove the inverse map of an injective linear function with closed graph from $U$ to $V$ (Banach spaces) is continuous iff the image is closed in $V$.

Counterexample of closed graph theorem when the image space is Hausdorff space but not compact?

Why is the derivative Operator defined over $C^2([-1,1])$ not closed?

A question about Banach spaces and closed graph theory

$C^1[0,1]$ is not banach using the closed graph theory

Proof of that the graph of subdifferential is closed when $f$ is closed proper convex function on $\mathbb{R}^n$.

How to determine mathematically that an expression with one independent variable forms a closed area or not

A linear operator $T$ is closed if and only if whenever $x_n\rightarrow x$ and $Tx_n\rightarrow y$, $y=Tx$.

Closed graph theorem for metric spaces

Application of Closed Graph Theorem for l2 space

Show that graphs of a contraction map and its inverse are both closed.

Question 2.18 from Brezis: Would someone help me to understand a solution given to this question?

On closed-graph theorem

How can I prove that this Linear operator is closed?

Accumulation point of a discrete Spectrum

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