Question

Does the multiplication operator $T_f$ given by $T_f\phi = f\phi$ have a discrete spectrum? Can a multiplication operator have continuous spectrum?

score 740 · Answer 1 · 2018-04-03 20:14:14

740

Views

Does the multiplication operator $T_f$ given by $T_f\phi = f\phi$ have a discrete spectrum? Can a multiplication operator have continuous spectrum?

Published on 03 Apr 2018 - 20:14

score 88 · Answer 2 · 2018-04-07 18:26:18

88

Views

Approximate spectrum of a linear operator on sequence

Published on 07 Apr 2018 - 18:26

score 43 · Answer 3 · 2026-03-25 06:09:55

43

Views

$E$ Banach space, $K: E \to E$ compact $\Rightarrow$ if $\lambda \neq 0 \in \sigma(K)$, $\lambda$ is eigenvalue

Published on 25 Mar 2026 - 6:09

score 283 · Answer 4 · 2026-03-25 05:07:06

283

Views

Prove $\|A\| \leq \|A\|_{HS}$, where $\|A\|$ is the operator norm of A

Published on 25 Mar 2026 - 5:07

score 437 · Answer 5 · 2026-03-25 06:00:22

437

Views

If an operator has a discrete spectrum eigenvalues, but infinitely many eigenvalues, are these necessarily countable?

Published on 25 Mar 2026 - 6:00

score 102 · Answer 6 · 2018-04-11 19:47:32

102

Views

Quotient of unital Banach algebra having no nonzero singular elements $\iff$ it has no nonzero proper ideal

Published on 11 Apr 2018 - 19:47

score 83 · Answer 7 · 2018-04-12 18:10:52

83

Views

Is spectral decomposition a differentiable function?

Published on 12 Apr 2018 - 18:10

score 342 · Answer 8 · 2018-04-15 14:05:39

342

Views

Spectral Theorem Multiplication Operator Version

Published on 15 Apr 2018 - 14:05

score 111 · Answer 9 · 2018-04-16 01:11:02

111

Views

Does the same operator norm imply the same spectral radius?

Published on 16 Apr 2018 - 1:11

score 1k · Answer 10 · 2018-04-17 09:56:46

1k

Views

Does a self-adjoint operator with discrete spectrum have compact resolvent?

Published on 17 Apr 2018 - 9:56

score 65 · Answer 11 · 2018-04-20 01:01:45

65

Views

On a question of projection in complex Hilbert space

Published on 20 Apr 2018 - 1:01

score 93 · Answer 12 · 2026-03-23 23:36:13

93

Views

How can Dirichlet eigenvalues be defined for closed sets?

Published on 23 Mar 2026 - 23:36

score 63 · Answer 13 · 2026-03-25 11:01:47

63

Views

Eigenvalues of Matrix Polynomials and transformations that leave them invariant

Published on 25 Mar 2026 - 11:01

score 533 · Answer 14 · 2018-04-22 23:05:12

533

Views

Finding the spectrum of an integral operator

Published on 22 Apr 2018 - 23:05

score 939 · Answer 15 · 2018-04-23 21:41:50

939

Views

Residual spectrum of the adjoint on Banach space

Published on 23 Apr 2018 - 21:41

List Question

Does the multiplication operator $T_f$ given by $T_f\phi = f\phi$ have a discrete spectrum? Can a multiplication operator have continuous spectrum?

Approximate spectrum of a linear operator on sequence

$E$ Banach space, $K: E \to E$ compact $\Rightarrow$ if $\lambda \neq 0 \in \sigma(K)$, $\lambda$ is eigenvalue

Prove $\|A\| \leq \|A\|_{HS}$, where $\|A\|$ is the operator norm of A

If an operator has a discrete spectrum eigenvalues, but infinitely many eigenvalues, are these necessarily countable?

Quotient of unital Banach algebra having no nonzero singular elements $\iff$ it has no nonzero proper ideal

Is spectral decomposition a differentiable function?

Spectral Theorem Multiplication Operator Version

Does the same operator norm imply the same spectral radius?

Does a self-adjoint operator with discrete spectrum have compact resolvent?

On a question of projection in complex Hilbert space

How can Dirichlet eigenvalues be defined for closed sets?

Eigenvalues of Matrix Polynomials and transformations that leave them invariant

Finding the spectrum of an integral operator

Residual spectrum of the adjoint on Banach space

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