Question

How can we prove that the space of trace class operators on a Hilbert space $H$ is the closure of $H\otimes H$ with respect to the trace norm?

score 1.9k · Answer 1 · 2016-05-12 18:19:57

1.9k

Views

How can we prove that the space of trace class operators on a Hilbert space $H$ is the closure of $H\otimes H$ with respect to the trace norm?

Published on 12 May 2016 - 18:19

score 154 · Answer 2 · 2026-03-27 13:17:41

154

Views

Symmetric block matrices with zero trace

Published on 27 Mar 2026 - 13:17

score 95 · Answer 3 · 2016-05-14 19:09:44

95

Views

The property that det(A) = prod of A's eigenvalues, and tr(A) = sum of A's eigenvalues

Published on 14 May 2016 - 19:09

score 1.6k · Answer 4 · 2016-05-16 10:46:20

1.6k

Views

Show that if $\operatorname{trace}(AB) = 0$ and $\operatorname{rank} (A)=1$ then $ABA=0$

Published on 16 May 2016 - 10:46

score 92 · Answer 5 · 2026-03-30 17:03:30

92

Views

Evaluate the product $\operatorname{tr}(AB)\operatorname{tr}(CB^{-1})$

Published on 30 Mar 2026 - 17:03

score 3k · Answer 6 · 2016-05-22 21:36:07

3k

Views

Generalized Poincaré Inequality on H1 proof.

Published on 22 May 2016 - 21:36

score 195 · Answer 7 · 2016-05-23 16:15:03

195

Views

unbounded solution, lim inf of trace,

Published on 23 May 2016 - 16:15

score 79 · Answer 8 · 2026-03-29 10:49:05

79

Views

Clever way to prove $\langle A,X\rangle=x^TAx$ with $X=xx^T$, $A\in S^n$?

Published on 29 Mar 2026 - 10:49

score 145 · Answer 9 · 2016-05-29 10:05:45

145

Views

Prove two complex matrices have null trace

Published on 29 May 2016 - 10:05

score 129 · Answer 10 · 2016-05-29 14:18:03

129

Views

$\sum_{k \geq 1} e^{it \sqrt{\lambda_k}}$ - Theory of distribution

Published on 29 May 2016 - 14:18

score 164 · Answer 11 · 2016-05-30 09:25:37

Given a matrix $A$ with $\operatorname{tr} (A) = 0$, prove that there is a B such that $\forall 1\leq i\leq n :(B^{-1}AB)_{i,i}=0$

score 390 · Answer 12 · 2016-06-06 17:53:04

390

Views

Can we write a matrix with zero trace as a commutator?

Published on 06 Jun 2016 - 17:53

score 35 · Answer 13 · 2016-06-08 02:42:44

35

Views

Need help to understand the derivation of Union of Square of 2 sets

Published on 08 Jun 2016 - 2:42

score 95 · Answer 14 · 2016-06-12 18:10:30

95

Views

Calculate the trace of $LBB^$, where $L:H→H$ and $B:=ΦT^{1/2}$ for some $Φ:U_0→H$, an embedding $ι:U_0→V$ and $T:=ιι^$

Published on 12 Jun 2016 - 18:10

score 34 · Answer 15 · 2016-06-14 20:38:42

34

Views

On the equivalence of two traces

Published on 14 Jun 2016 - 20:38

List Question

How can we prove that the space of trace class operators on a Hilbert space $H$ is the closure of $H\otimes H$ with respect to the trace norm?

Symmetric block matrices with zero trace

The property that det(A) = prod of A's eigenvalues, and tr(A) = sum of A's eigenvalues

Show that if $\operatorname{trace}(AB) = 0$ and $\operatorname{rank} (A)=1$ then $ABA=0$

Evaluate the product $\operatorname{tr}(AB)\operatorname{tr}(CB^{-1})$

Generalized Poincaré Inequality on H1 proof.

unbounded solution, lim inf of trace,

Clever way to prove $\langle A,X\rangle=x^TAx$ with $X=xx^T$, $A\in S^n$?

Prove two complex matrices have null trace

$\sum_{k \geq 1} e^{it \sqrt{\lambda_k}}$ - Theory of distribution

Given a matrix $A$ with $\operatorname{tr} (A) = 0$, prove that there is a B such that $\forall 1\leq i\leq n :(B^{-1}AB)_{i,i}=0$

Can we write a matrix with zero trace as a commutator?

Need help to understand the derivation of Union of Square of 2 sets

Calculate the trace of $LBB^$, where $L:H→H$ and $B:=ΦT^{1/2}$ for some $Φ:U_0→H$, an embedding $ι:U_0→V$ and $T:=ιι^$

On the equivalence of two traces

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