Question

Let A ∈ B(H) be self-adjoint and $f$ is a positive continuous function on $\sigma(A)$, Show $f(A)$ is a positive operator

score 288 · Answer 1 · 2026-04-10 14:03:33

288

Views

Let A ∈ B(H) be self-adjoint and $f$ is a positive continuous function on $\sigma(A)$, Show $f(A)$ is a positive operator

Published on 10 Apr 2026 - 14:03

score 119 · Answer 2 · 2026-04-13 23:47:13

119

Views

In a C* algebra, bounded linear functional + norm condition => positive

Published on 13 Apr 2026 - 23:47

score 52 · Answer 3 · 2026-04-13 23:50:18

52

Views

Continuity of $*$-map under different topology on $B(H)$

Published on 13 Apr 2026 - 23:50

score 102 · Answer 4 · 2026-04-10 19:54:35

102

Views

Do *-homomorphisms have support projections?

Published on 10 Apr 2026 - 19:54

score 131 · Answer 5 · 2026-04-14 04:17:22

131

Views

How to prove that the tensor product of C*-algebras $A \otimes_{\alpha} B$ is simple iff $\alpha$ is the spatial norm and both $A$ and $B$ are simple?

Published on 14 Apr 2026 - 4:17

score 81 · Answer 6 · 2026-04-09 03:42:14

81

Views

Is every projection in the bidual a spectral projection of a self-adjoint operator?

Published on 09 Apr 2026 - 3:42

score 50 · Answer 7 · 2026-04-14 15:24:39

50

Views

In a $C^*$ algebra, if $A\geq B\geq 0$ then $A^{\frac{1}{2}}\geq B^{\frac{1}{2}}$

Published on 14 Apr 2026 - 15:24

score 111 · Answer 8 · 2026-04-14 14:10:39

111

Views

Showing that $M_n(\mathbb{C})$ is a unital C*-algebra

Published on 14 Apr 2026 - 14:10

score 50 · Answer 9 · 2026-04-13 23:50:25

50

Views

Is the left invertible element unique in Banach algebras?

Published on 13 Apr 2026 - 23:50

score 209 · Answer 10 · 2026-04-13 23:52:54

209

Views

$X$, $Y$ homeomorphic compact Hausdorff spaces then $C(X)$ and $C(Y)$ are $\ast$-isomorphic unital $C^\ast$-algebras

Published on 13 Apr 2026 - 23:52

score 123 · Answer 11 · 2026-04-13 01:39:52

123

Views

Unital $C^\ast$-algebra $\mathcal{A}$ with positive elements $\mathcal{A}$.

Published on 13 Apr 2026 - 1:39

score 96 · Answer 12 · 2026-04-16 01:45:03

96

Views

Self-adjoint elements $A_1$ and $A_2$ in a $C^\ast$-algebra

Published on 16 Apr 2026 - 1:45

score 57 · Answer 13 · 2026-04-11 10:40:07

57

Views

$a \le \|a\|$ in a von Neumann algebra

Published on 11 Apr 2026 - 10:40

score 79 · Answer 14 · 2026-04-09 04:55:44

79

Views

Trying to understand a proof from an article

Published on 09 Apr 2026 - 4:55

score 32 · Answer 15 · 2026-04-16 22:28:44

32

Views

An AF $C^*$ algebra has an approximate identity consisting of projections

Published on 16 Apr 2026 - 22:28

List Question

Let A ∈ B(H) be self-adjoint and $f$ is a positive continuous function on $\sigma(A)$, Show $f(A)$ is a positive operator

In a C* algebra, bounded linear functional + norm condition => positive

Continuity of $*$-map under different topology on $B(H)$

Do *-homomorphisms have support projections?

How to prove that the tensor product of C*-algebras $A \otimes_{\alpha} B$ is simple iff $\alpha$ is the spatial norm and both $A$ and $B$ are simple?

Is every projection in the bidual a spectral projection of a self-adjoint operator?

In a $C^*$ algebra, if $A\geq B\geq 0$ then $A^{\frac{1}{2}}\geq B^{\frac{1}{2}}$

Showing that $M_n(\mathbb{C})$ is a unital C*-algebra

Is the left invertible element unique in Banach algebras?

$X$, $Y$ homeomorphic compact Hausdorff spaces then $C(X)$ and $C(Y)$ are $\ast$-isomorphic unital $C^\ast$-algebras

Unital $C^\ast$-algebra $\mathcal{A}$ with positive elements $\mathcal{A}$.

Self-adjoint elements $A_1$ and $A_2$ in a $C^\ast$-algebra

$a \le \|a\|$ in a von Neumann algebra

Trying to understand a proof from an article

An AF $C^*$ algebra has an approximate identity consisting of projections

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