List questions from closed-graph

Published on 25 Mar 2026 - 10:52

58

Views

How to disprove $(\text B)$ and $(\text D)$?

Published on 25 Dec 2019 - 8:32

38

Views

Showing that a map is open by usying lower boundedness of adjoint

Published on 03 Jan 2020 - 14:04

563

Views

Equivalence between closed range + finite dimensional kernel, and a statement about sequences.

Published on 08 Feb 2020 - 23:20

71

Views

If a sequence of $C^2$ function converges in $L^2$, then what happens to the differential images of them?

Published on 11 Feb 2020 - 9:33

282

Views

Whenever $f=T(x)$ then $f(x) \geq 0$. Prove $T$ is bounded by closed graph theorem.

Published on 24 Feb 2020 - 6:25

127

Views

the graph of any continuous map is closed on Banach spaces.

Published on 02 Mar 2020 - 18:52

83

Views

prove that $\Lambda(S)$ is closed for every closed set $S \subset X$

Published on 03 Mar 2020 - 3:37

538

Views

How to prove that the graph of this operator is closed?

Published on 01 Apr 2020 - 13:12

470

Views

Graph of a discontinuous function is closed

Published on 02 Apr 2020 - 5:47

446

Views

Let X be a Banach space and show the series converges.

Published on 25 Apr 2020 - 20:32

587

Views

Weakening the assumptions of the Hellinger-Toeplitz theorem

Published on 06 May 2020 - 18:51

34

Views

Is every closed operator a bijection?

Published on 22 Jun 2020 - 10:18

1.5k

Views

Continuity of correspondence - Hemi-continuity

Published on 28 Jun 2020 - 17:39

1.3k

Views

Closed graph theorem; exercise

Published on 19 Jul 2016 - 9:47

List Question

Unbounded operator such that $P^2=P$

How to disprove $(\text B)$ and $(\text D)$?

Showing that a map is open by usying lower boundedness of adjoint

Equivalence between closed range + finite dimensional kernel, and a statement about sequences.

If a sequence of $C^2$ function converges in $L^2$, then what happens to the differential images of them?

Whenever $f=T(x)$ then $f(x) \geq 0$. Prove $T$ is bounded by closed graph theorem.

the graph of any continuous map is closed on Banach spaces.

prove that $\Lambda(S)$ is closed for every closed set $S \subset X$

How to prove that the graph of this operator is closed?

Graph of a discontinuous function is closed

Let X be a Banach space and show the series converges.

Weakening the assumptions of the Hellinger-Toeplitz theorem

Is every closed operator a bijection?

Continuity of correspondence - Hemi-continuity

Closed graph theorem; exercise

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