Question

$M(\rho)=\operatorname{Tr}_2\left(\ U\ \rho\otimes\rho_2\ U^{\dagger}\right)$is unitary $\iff\ U=U_1\otimes U_2$, a product of $2$ unitary operators?

score 26 · Answer 1 · 2026-04-16 09:30:47

26

Views

$M(\rho)=\operatorname{Tr}_2\left(\ U\ \rho\otimes\rho_2\ U^{\dagger}\right)$is unitary $\iff\ U=U_1\otimes U_2$, a product of $2$ unitary operators?

Published on 16 Apr 2026 - 9:30

score 38 · Answer 2 · 2026-04-15 21:52:55

38

Views

If $A_n$ is a compact operator, determine the singular values of the product $A_n\cdots A_1$

Published on 15 Apr 2026 - 21:52

score 221 · Answer 3 · 2026-04-12 04:38:50

221

Views

Example for a polynomially compact operator

Published on 12 Apr 2026 - 4:38

score 82 · Answer 4 · 2026-03-27 10:09:36

82

Views

Question concerning proof of unique existence of adjoint operator

Published on 27 Mar 2026 - 10:09

score 177 · Answer 5 · 2026-04-12 15:20:30

177

Views

Functional Kreyszig section 7.3 exercise 8

Published on 12 Apr 2026 - 15:20

score 212 · Answer 6 · 2026-04-08 23:26:50

212

Views

About an inequality between the real part and absolute value of an operator

Published on 08 Apr 2026 - 23:26

score 56 · Answer 7 · 2026-04-16 01:18:13

56

Views

The relation between the separability and cardinality of a Banach space

Published on 16 Apr 2026 - 1:18

score 98 · Answer 8 · 2026-04-14 18:00:29

98

Views

If $A$ is compact and self-adjoint, then $A=U^\ast DU$ for some orthogonal $U$ and diagonal $D$

Published on 14 Apr 2026 - 18:00

score 206 · Answer 9 · 2026-04-09 20:47:42

206

Views

Norm and eigenvalues of a multiplication operator

Published on 09 Apr 2026 - 20:47

score 44 · Answer 10 · 2026-04-11 11:46:29

44

Views

Property of spectrum

Published on 11 Apr 2026 - 11:46

score 51 · Answer 11 · 2026-04-10 10:02:01

51

Views

Is it possible to find a basis for a non-compact operator?

Published on 10 Apr 2026 - 10:02

score 127 · Answer 12 · 2026-04-12 22:45:15

127

Views

Relate the $k$th singular value of a compact operator $A$ to the tensor-product $A^{\otimes k}$

Published on 12 Apr 2026 - 22:45

score 44 · Answer 13 · 2026-04-13 18:05:44

44

Views

Algebraic dimension of the dual of $\ell^{\infty}$

Published on 13 Apr 2026 - 18:05

score 108 · Answer 14 · 2026-04-14 21:34:07

108

Views

Point and continuous spectrum of a multiplication operator in $L^2(\mathbb{R})$

Published on 14 Apr 2026 - 21:34

score 45 · Answer 15 · 2026-04-16 04:48:19

45

Views

Compute $\|T\|_1$, $\|T\|_2$ and $\|T\|$

Published on 16 Apr 2026 - 4:48

List Question

$M(\rho)=\operatorname{Tr}_2\left(\ U\ \rho\otimes\rho_2\ U^{\dagger}\right)$is unitary $\iff\ U=U_1\otimes U_2$, a product of $2$ unitary operators?

If $A_n$ is a compact operator, determine the singular values of the product $A_n\cdots A_1$

Example for a polynomially compact operator

Question concerning proof of unique existence of adjoint operator

Functional Kreyszig section 7.3 exercise 8

About an inequality between the real part and absolute value of an operator

The relation between the separability and cardinality of a Banach space

If $A$ is compact and self-adjoint, then $A=U^\ast DU$ for some orthogonal $U$ and diagonal $D$

Norm and eigenvalues of a multiplication operator

Property of spectrum

Is it possible to find a basis for a non-compact operator?

Relate the $k$th singular value of a compact operator $A$ to the tensor-product $A^{\otimes k}$

Algebraic dimension of the dual of $\ell^{\infty}$

Point and continuous spectrum of a multiplication operator in $L^2(\mathbb{R})$

Compute $\|T\|_1$, $\|T\|_2$ and $\|T\|$

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