Question

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

score 798 · Answer 1 · 2018-07-12 17:17:15

798

Views

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

Published on 12 Jul 2018 - 17:17

score 75 · Answer 2 · 2018-07-12 22:25:12

75

Views

Exercises on derivative operator on subspaces of $L^2$

Published on 12 Jul 2018 - 22:25

score 242 · Answer 3 · 2018-07-13 14:49:15

242

Views

Unitarily equivalent operators have unitarily equivalent spectral measures

Published on 13 Jul 2018 - 14:49

score 39 · Answer 4 · 2018-07-14 07:50:06

39

Views

Direct sum of quasi-nilpotent part of an operator

Published on 14 Jul 2018 - 7:50

score 609 · Answer 5 · 2018-07-17 10:35:03

609

Views

Eigenvalues of a kernel integral operator

Published on 17 Jul 2018 - 10:35

score 28 · Answer 6 · 2018-07-17 10:35:50

28

Views

Characterization of spectral measures: Error in exercise?

Published on 17 Jul 2018 - 10:35

score 256 · Answer 7 · 2026-03-25 01:21:18

256

Views

Spectrum of two operators

Published on 25 Mar 2026 - 1:21

score 70 · Answer 8 · 2018-07-21 02:42:07

70

Views

A very interesting property of symmetric positive definite matrix. Need proof! (Citation needed)

Published on 21 Jul 2018 - 2:42

score 49 · Answer 9 · 2026-03-25 15:37:50

49

Views

Why is $E$ open in $D$?

Published on 25 Mar 2026 - 15:37

score 99 · Answer 10 · 2026-03-25 17:44:39

99

Views

If $|A_{ij}|\leq 1$ for all entries of symmetric $A$, then the largest possible spectral norm of $A$ is smaller than $n$?

Published on 25 Mar 2026 - 17:44

score 574 · Answer 11 · 2026-03-20 06:46:29

574

Views

If matrix $A$ has entries $A_{ij}=\sin(\theta_i - \theta_j)$, why does $\|A\|_* = n$ always hold?

Published on 20 Mar 2026 - 6:46

score 115 · Answer 12 · 2026-03-25 19:04:24

115

Views

If $r(a) < 1$, does $\sum_{n=0}^\infty a^{*n}a^n$ necessarily converge?

Published on 25 Mar 2026 - 19:04

score 63 · Answer 13 · 2018-07-30 03:41:49

If the point spectrum of some operator is made up of 4 values, $\{1,2,3,4\}$ does that mean that all numbers in $[1,4]$ are in the spectrum?

score 575 · Answer 14 · 2018-07-30 04:10:15

575

Views

Does an infinite dimensional operator $T$ having an eigenvalue of $0$ imply that $T^{-1}$ doesn't exist?

Published on 30 Jul 2018 - 4:10

score 117 · Answer 15 · 2018-07-30 05:51:10

117

Views

Verification of the values in the continuous spectrum of an operator

Published on 30 Jul 2018 - 5:51

List Question

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

Exercises on derivative operator on subspaces of $L^2$

Unitarily equivalent operators have unitarily equivalent spectral measures

Direct sum of quasi-nilpotent part of an operator

Eigenvalues of a kernel integral operator

Characterization of spectral measures: Error in exercise?

Spectrum of two operators

A very interesting property of symmetric positive definite matrix. Need proof! (Citation needed)

Why is $E$ open in $D$?

If $|A_{ij}|\leq 1$ for all entries of symmetric $A$, then the largest possible spectral norm of $A$ is smaller than $n$?

If matrix $A$ has entries $A_{ij}=\sin(\theta_i - \theta_j)$, why does $\|A\|_* = n$ always hold?

If $r(a) < 1$, does $\sum_{n=0}^\infty a^{*n}a^n$ necessarily converge?

If the point spectrum of some operator is made up of 4 values, $\{1,2,3,4\}$ does that mean that all numbers in $[1,4]$ are in the spectrum?

Does an infinite dimensional operator $T$ having an eigenvalue of $0$ imply that $T^{-1}$ doesn't exist?

Verification of the values in the continuous spectrum of an operator

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