Question

If the derivative of a continuously differentiable functions between Banach spaces at a point is an isomorphism, is it so also in a neighborhood?

score 44 · Answer 1 · 2020-04-29 07:47:37

44

Views

If the derivative of a continuously differentiable functions between Banach spaces at a point is an isomorphism, is it so also in a neighborhood?

Published on 29 Apr 2020 - 7:47

score 374 · Answer 2 · 2026-03-24 12:15:10

374

Views

Proving $\operatorname{coker}(f^) \cong (\ker f)^$ for a linear map $f$

Published on 24 Mar 2026 - 12:15

score 99 · Answer 3 · 2020-05-02 00:55:38

99

Views

Dual Spaces Isomorphism

Published on 02 May 2020 - 0:55

score 51 · Answer 4 · 2020-05-05 14:42:26

51

Views

Difference between $T \colon V \to W $ and $ T \colon V \to V $ for $\dim(V) = \dim(W)$.

Published on 05 May 2020 - 14:42

score 37 · Answer 5 · 2020-05-09 18:36:32

37

Views

Proof verification: $V \cong \mathscr{L}(\mathbb{F}, V)$

Published on 09 May 2020 - 18:36

score 242 · Answer 6 · 2020-05-10 03:46:58

242

Views

How do I determine whether or not an isomorphism $T:V\to W$ is a canonical isomorphism?

Published on 10 May 2020 - 3:46

score 462 · Answer 7 · 2020-05-11 13:28:08

462

Views

$T(p(x)) = p'(x)$ is an isomorphism

Published on 11 May 2020 - 13:28

score 63 · Answer 8 · 2020-05-18 14:04:42

63

Views

Is $f - 3I$ an isomorphism if $f$ is orthogonal?

Published on 18 May 2020 - 14:04

score 76 · Answer 9 · 2020-05-28 21:25:46

76

Views

I don't understand the Rank–nullity theorem..

Published on 28 May 2020 - 21:25

score 275 · Answer 10 · 2020-06-02 14:58:44

275

Views

Isomorphism between tensor product of Hilbert spaces

Published on 02 Jun 2020 - 14:58

score 132 · Answer 11 · 2020-06-04 16:46:07

132

Views

Show that the statements about maps are equivalent

Published on 04 Jun 2020 - 16:46

score 293 · Answer 12 · 2020-06-05 00:17:35

293

Views

Is it true that $T$ is orthogonal if and only if $T$ is isomorphism?

Published on 05 Jun 2020 - 0:17

score 549 · Answer 13 · 2020-06-05 05:10:43

549

Views

Are orthogonal operators always isomorphisms?

Published on 05 Jun 2020 - 5:10

score 473 · Answer 14 · 2026-02-23 01:05:11

473

Views

An isomorphism between two normed vector spaces with the same finite dimension is an homeomorphism

Published on 23 Feb 2026 - 1:05

score 1k · Answer 15 · 2020-06-07 19:48:52

1k

Views

Intuition behind Isomorphic spaces "Being the Same"

Published on 07 Jun 2020 - 19:48

List Question

If the derivative of a continuously differentiable functions between Banach spaces at a point is an isomorphism, is it so also in a neighborhood?

Proving $\operatorname{coker}(f^) \cong (\ker f)^$ for a linear map $f$

Dual Spaces Isomorphism

Difference between $T \colon V \to W $ and $ T \colon V \to V $ for $\dim(V) = \dim(W)$.

Proof verification: $V \cong \mathscr{L}(\mathbb{F}, V)$

How do I determine whether or not an isomorphism $T:V\to W$ is a canonical isomorphism?

$T(p(x)) = p'(x)$ is an isomorphism

Is $f - 3I$ an isomorphism if $f$ is orthogonal?

I don't understand the Rank–nullity theorem..

Isomorphism between tensor product of Hilbert spaces

Show that the statements about maps are equivalent

Is it true that $T$ is orthogonal if and only if $T$ is isomorphism?

Are orthogonal operators always isomorphisms?

An isomorphism between two normed vector spaces with the same finite dimension is an homeomorphism

Intuition behind Isomorphic spaces "Being the Same"

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