Question

Positive elements in $C^*$-algebras (given a positive element, finding a smaller positive element in a bigger algebra)

score 71 · Answer 1 · 2023-05-13 11:26:34

71

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Positive elements in $C^*$-algebras (given a positive element, finding a smaller positive element in a bigger algebra)

Published on 13 May 2023 - 11:26

score 79 · Answer 2 · 2023-05-13 22:26:52

79

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Image of the natural embedding of a normed linear space

Published on 13 May 2023 - 22:26

score 57 · Answer 3 · 2023-05-15 03:41:59

57

Views

Characterisation of non-closed ideals in $C[0,1]$

Published on 15 May 2023 - 3:41

score 59 · Answer 4 · 2026-03-29 07:29:09

59

Views

(Dis-)continuity of the multiplication in the space $\mathcal{B}(\mathcal{H})$ of bounded linear operators on a Hilbert space

Published on 29 Mar 2026 - 7:29

score 27 · Answer 5 · 2026-03-25 21:49:26

27

Views

The Elliot invariant and the opposite algebra

Published on 25 Mar 2026 - 21:49

score 77 · Answer 6 · 2026-03-25 21:45:57

77

Views

Unitary element in $M_2(A)$

Published on 25 Mar 2026 - 21:45

score 75 · Answer 7 · 2023-05-19 07:52:30

75

Views

Every finite rank operator on a Hilbert space can be written $\sum_{j=1}^n s_j|u_j\rangle\langle v_j|$ with $\{u_j\},\{v_j\}$ orthonormal

Published on 19 May 2023 - 7:52

score 58 · Answer 8 · 2023-05-21 07:53:04

58

Views

An inequality involving states and positive linear functional on a $C^*$-algebra

Published on 21 May 2023 - 7:53

score 70 · Answer 9 · 2026-03-26 06:31:45

70

Views

If an element $b$ of a $C^*$-algebra $B$ is self-adjoint with $\delta=\|b-b^2\|<\frac14$ then there is a projection $p\in B$ with $\|b-p\|\leq2\delta$

Published on 26 Mar 2026 - 6:31

score 64 · Answer 10 · 2026-03-25 21:49:54

Consider inductive sequence of $C^\ast$-algebra $A_1 \overset{φ_1}→A_2\overset{φ_2}→···$ inductive limit $(A,(μ_n)_n∈ℕ)$. How is $K_{0}$ continous?

score 60 · Answer 11 · 2026-03-25 21:49:01

60

Views

Show that $δ_1([u]_1) = [e]_0−[f]_0$, where $e, f∈M_2(C_0(ℝ^2)^∼)$.

Published on 25 Mar 2026 - 21:49

score 42 · Answer 12 · 2026-03-25 21:50:00

42

Views

Show that there is a natural number n and a projection ∈(̃ ) such that =[]0−[()]0 and ̃ ()∼ℎ((̃ )) .

Published on 25 Mar 2026 - 21:50

score 35 · Answer 13 · 2023-05-25 15:59:34

35

Views

Standard form of $B(H)$

Published on 25 May 2023 - 15:59

score 76 · Answer 14 · 2023-05-25 19:35:58

76

Views

Show that $Γ$ is the one-element group.

Published on 25 May 2023 - 19:35

score 103 · Answer 15 · 2026-03-30 09:34:30

103

Views

Power rule for derivative operator $D^n$

Published on 30 Mar 2026 - 9:34

List Question

Positive elements in $C^*$-algebras (given a positive element, finding a smaller positive element in a bigger algebra)

Image of the natural embedding of a normed linear space

Characterisation of non-closed ideals in $C[0,1]$

(Dis-)continuity of the multiplication in the space $\mathcal{B}(\mathcal{H})$ of bounded linear operators on a Hilbert space

The Elliot invariant and the opposite algebra

Unitary element in $M_2(A)$

Every finite rank operator on a Hilbert space can be written $\sum_{j=1}^n s_j|u_j\rangle\langle v_j|$ with $\{u_j\},\{v_j\}$ orthonormal

An inequality involving states and positive linear functional on a $C^*$-algebra

If an element $b$ of a $C^*$-algebra $B$ is self-adjoint with $\delta=\|b-b^2\|<\frac14$ then there is a projection $p\in B$ with $\|b-p\|\leq2\delta$

Consider inductive sequence of $C^\ast$-algebra $A_1 \overset{φ_1}→A_2\overset{φ_2}→···$ inductive limit $(A,(μ_n)_n∈ℕ)$. How is $K_{0}$ continous?

Show that $δ_1([u]_1) = [e]_0−[f]_0$, where $e, f∈M_2(C_0(ℝ^2)^∼)$.

Show that there is a natural number n and a projection ∈(̃ ) such that =[]0−[()]0 and ̃ ()∼ℎ((̃ )) .

Standard form of $B(H)$

Show that $Γ$ is the one-element group.

Power rule for derivative operator $D^n$

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