Question

Does the inclusion $A \subset B$ for closed densely defined operators $A$ and $B$ imply $A=B$?

score 361 · Answer 1 · 2018-07-11 11:17:36

361

Views

Does the inclusion $A \subset B$ for closed densely defined operators $A$ and $B$ imply $A=B$?

Published on 11 Jul 2018 - 11:17

score 162 · Answer 2 · 2018-07-11 19:42:45

162

Views

Sum of a closed range operator and a non closed range operator

Published on 11 Jul 2018 - 19:42

score 131 · Answer 3 · 2026-03-25 17:37:06

131

Views

$C^*$ algebra has a nonzero finite dimensional quotient

Published on 25 Mar 2026 - 17:37

score 799 · Answer 4 · 2026-03-25 23:38:47

799

Views

Is the spectrum of an unbounded self-adjoint operator always an unbounded set?

Published on 25 Mar 2026 - 23:38

score 65 · Answer 5 · 2026-03-25 12:53:18

65

Views

Comparing bounded and compact operators on $L^2$ to Roe algebras

Published on 25 Mar 2026 - 12:53

score 529 · Answer 6 · 2026-03-26 11:16:57

529

Views

Example of hyponormal operator which is not normal

Published on 26 Mar 2026 - 11:16

score 1.4k · Answer 7 · 2026-03-25 09:26:18

1.4k

Views

Closed graph theorem seems to state that a closed operator has to be bounded?

Published on 25 Mar 2026 - 9:26

score 223 · Answer 8 · 2026-03-25 14:23:34

223

Views

Are two projections which are Murray-von-Neumann equivalent in $C(X,M_{n})$ approximately unitarily equivalent?

Published on 25 Mar 2026 - 14:23

score 243 · Answer 9 · 2026-03-26 01:00:09

243

Views

Unitarily equivalent operators have unitarily equivalent spectral measures

Published on 26 Mar 2026 - 1:00

score 81 · Answer 10 · 2026-03-25 14:28:50

81

Views

Finite dimensional $C^*$ algebra

Published on 25 Mar 2026 - 14:28

score 30 · Answer 11 · 2018-07-13 18:10:41

30

Views

Why does $\|(op)\|_{L^2{\infty} \rightarrow L^2{\infty}} \leq \frac{1}{2}$ $\implies$ $op$ is invertible?

Published on 13 Jul 2018 - 18:10

score 40 · Answer 12 · 2026-03-25 23:39:21

40

Views

Direct sum of quasi-nilpotent part of an operator

Published on 25 Mar 2026 - 23:39

score 106 · Answer 13 · 2018-07-15 08:25:34

106

Views

$F(y) = F(x)$ for aribtrary continuous linear functional $F$, then by Hahn-Banach $y=x$?

Published on 15 Jul 2018 - 8:25

score 41 · Answer 14 · 2026-03-26 21:27:08

41

Views

Why is $A$ on the left hand side yet $B$ is on the right hand side when we evaluate $ \frac{d}{dt}(e^{tA}Ce^{tB}) = Ae^{tA}Ce^{tB} + e^{tA}Ce^{tB}B$?

Published on 26 Mar 2026 - 21:27

score 1.1k · Answer 15 · 2026-03-25 03:01:20

1.1k

Views

Quadratic form associated to a linear operator in an Hilbert space

Published on 25 Mar 2026 - 3:01

List Question

Does the inclusion $A \subset B$ for closed densely defined operators $A$ and $B$ imply $A=B$?

Sum of a closed range operator and a non closed range operator

$C^*$ algebra has a nonzero finite dimensional quotient

Is the spectrum of an unbounded self-adjoint operator always an unbounded set?

Comparing bounded and compact operators on $L^2$ to Roe algebras

Example of hyponormal operator which is not normal

Closed graph theorem seems to state that a closed operator has to be bounded?

Are two projections which are Murray-von-Neumann equivalent in $C(X,M_{n})$ approximately unitarily equivalent?

Unitarily equivalent operators have unitarily equivalent spectral measures

Finite dimensional $C^*$ algebra

Why does $\|(op)\|_{L^2{\infty} \rightarrow L^2{\infty}} \leq \frac{1}{2}$ $\implies$ $op$ is invertible?

Direct sum of quasi-nilpotent part of an operator

$F(y) = F(x)$ for aribtrary continuous linear functional $F$, then by Hahn-Banach $y=x$?

Why is $A$ on the left hand side yet $B$ is on the right hand side when we evaluate $ \frac{d}{dt}(e^{tA}Ce^{tB}) = Ae^{tA}Ce^{tB} + e^{tA}Ce^{tB}B$?

Quadratic form associated to a linear operator in an Hilbert space

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