Question

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

score 801 · Answer 1 · 2026-04-10 22:58:14

801

Views

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

Published on 10 Apr 2026 - 22:58

score 79 · Answer 2 · 2026-05-11 00:28:26

79

Views

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

Published on 11 May 2026 - 0:28

score 245 · Answer 3 · 2026-04-10 18:46:50

245

Views

Unitarily equivalent operators have unitarily equivalent spectral measures

Published on 10 Apr 2026 - 18:46

score 42 · Answer 4 · 2026-04-10 17:04:59

42

Views

Direct sum of quasi-nilpotent part of an operator

Published on 10 Apr 2026 - 17:04

score 612 · Answer 5 · 2026-04-09 10:50:34

612

Views

Eigenvalues of a kernel integral operator

Published on 09 Apr 2026 - 10:50

score 31 · Answer 6 · 2026-04-11 04:44:34

31

Views

Characterization of spectral measures: Error in exercise?

Published on 11 Apr 2026 - 4:44

score 260 · Answer 7 · 2026-05-10 15:59:25

260

Views

Spectrum of two operators

Published on 10 May 2026 - 15:59

score 73 · Answer 8 · 2026-04-12 02:46:00

73

Views

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

Published on 12 Apr 2026 - 2:46

score 54 · Answer 9 · 2026-05-10 17:07:43

54

Views

Why is $E$ open in $D$?

Published on 10 May 2026 - 17:07

score 102 · Answer 10 · 2026-05-10 14:49:16

102

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 10 May 2026 - 14:49

score 580 · Answer 11 · 2026-04-29 12:41:04

580

Views

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

Published on 29 Apr 2026 - 12:41

score 116 · Answer 12 · 2026-04-15 06:17:44

116

Views

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

Published on 15 Apr 2026 - 6:17

score 66 · Answer 13 · 2026-04-13 17:11:26

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 577 · Answer 14 · 2026-04-14 04:18:25

577

Views

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

Published on 14 Apr 2026 - 4:18

score 120 · Answer 15 · 2026-04-11 14:15:28

120

Views

Verification of the values in the continuous spectrum of an operator

Published on 11 Apr 2026 - 14:15

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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