Question

Isomorphism Between the Sequence Spaces $c$ and $c_o$

score 191 · Answer 1 · 2023-04-30 22:26:31

191

Views

Isomorphism Between the Sequence Spaces $c$ and $c_o$

Published on 30 Apr 2023 - 22:26

score 80 · Answer 2 · 2023-05-01 13:33:22

80

Views

Proof that f : V* ⊗ W −→ HomK (V, W ) is an isomorphism

Published on 01 May 2023 - 13:33

score 63 · Answer 3 · 2023-05-03 01:24:39

63

Views

Can we prove that $\psi : V \rightarrow V^{**}$ is an isomorphism by constructing an inverse map?

Published on 03 May 2023 - 1:24

score 31 · Answer 4 · 2023-05-06 12:42:02

31

Views

If $V\cong W$ and $U\subseteq V$, is $U\cong T(U)$?

Published on 06 May 2023 - 12:42

score 68 · Answer 5 · 2023-05-06 13:00:50

68

Views

Applying the double dual isomorphism $V\cong V’’$

Published on 06 May 2023 - 13:00

score 230 · Answer 6 · 2023-05-12 23:41:26

230

Views

Suppose $T_1, T_2\in L(V,W)$. Prove that if $\text{null }T_1=\text{null }T_2$ then there exists invertible operator $S\in L(W)$ such that $T_1=ST_2$

Published on 12 May 2023 - 23:41

score 96 · Answer 7 · 2023-05-20 03:55:38

96

Views

Dimension, Orbits, G-morphisms, Function Spaces, Finite Groups

Published on 20 May 2023 - 3:55

score 53 · Answer 8 · 2023-05-22 11:38:28

53

Views

Assume $A \oplus B \cong A \oplus C$. Is $B \cong C$?

Published on 22 May 2023 - 11:38

score 40 · Answer 9 · 2023-05-25 13:02:40

40

Views

Isomorphism theorems to conclude that cokernel is finite dimensional

Published on 25 May 2023 - 13:02

score 60 · Answer 10 · 2026-03-21 20:25:02

60

Views

Relation between $\mathbb{Q}$ and $\mathbb{Z}^2$

Published on 21 Mar 2026 - 20:25

score 92 · Answer 11 · 2023-06-01 16:47:44

92

Views

Clifford algebra $Cl_1 \cong \mathbb{C}$

Published on 01 Jun 2023 - 16:47

score 45 · Answer 12 · 2026-03-25 23:43:59

45

Views

$(\ell^{1})^{*}$ isometrically isomorphic to $\ell^{\infty}$ as a corollary of Riesz representation Theorem.

Published on 25 Mar 2026 - 23:43

score 60 · Answer 13 · 2023-06-10 12:20:43

60

Views

Confusion on proof of existence of ismophism between bilinear form on $L$ and dual space $\mathcal{L}(L,L^*)$

Published on 10 Jun 2023 - 12:20

score 120 · Answer 14 · 2023-06-19 23:01:43

120

Views

Dual of the annihilator isomorphic to quotient space

Published on 19 Jun 2023 - 23:01

score 97 · Answer 15 · 2023-06-21 17:33:08

97

Views

If $A$ is a bounded linear operator and positive on a Hilbert space. Show that $A+\lambda I$ is an isomorphism $\forall\lambda>0$.

Published on 21 Jun 2023 - 17:33

List Question

Isomorphism Between the Sequence Spaces $c$ and $c_o$

Proof that f : V* ⊗ W −→ HomK (V, W ) is an isomorphism

Can we prove that $\psi : V \rightarrow V^{**}$ is an isomorphism by constructing an inverse map?

If $V\cong W$ and $U\subseteq V$, is $U\cong T(U)$?

Applying the double dual isomorphism $V\cong V’’$

Suppose $T_1, T_2\in L(V,W)$. Prove that if $\text{null }T_1=\text{null }T_2$ then there exists invertible operator $S\in L(W)$ such that $T_1=ST_2$

Dimension, Orbits, G-morphisms, Function Spaces, Finite Groups

Assume $A \oplus B \cong A \oplus C$. Is $B \cong C$?

Isomorphism theorems to conclude that cokernel is finite dimensional

Relation between $\mathbb{Q}$ and $\mathbb{Z}^2$

Clifford algebra $Cl_1 \cong \mathbb{C}$

$(\ell^{1})^{*}$ isometrically isomorphic to $\ell^{\infty}$ as a corollary of Riesz representation Theorem.

Confusion on proof of existence of ismophism between bilinear form on $L$ and dual space $\mathcal{L}(L,L^*)$

Dual of the annihilator isomorphic to quotient space

If $A$ is a bounded linear operator and positive on a Hilbert space. Show that $A+\lambda I$ is an isomorphism $\forall\lambda>0$.

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