List questions from operator-theory

Published on 13 Apr 2026 - 14:16

57

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If $X$ is a finite dimensional Hilbert Space, $A$ a bounded operator on $X$, then is $||A||_{op} \leq \rho(A)$?

Published on 14 Apr 2026 - 11:51

146

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Is the space of all bounded linear operators a subspace of the space of the linear operators?

Published on 10 Apr 2026 - 23:15

410

Views

Weak-* closed ideal of $L^\infty$

Published on 12 Apr 2026 - 12:27

310

Views

How to show the following operator is linear?

Published on 10 Apr 2026 - 4:11

82

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Local linear operator in physical and Fourier space

Published on 11 Apr 2026 - 18:18

321

Views

show that the eigenspace corresponding to every $\lambda_n$ is one dimensional

Published on 16 Apr 2026 - 4:14

227

Views

Is the operator compact or bijective?

Published on 11 Apr 2026 - 10:52

348

Views

Obtaining Hamiltonian Matrix from Operators (Dirac Notation)

Published on 12 Apr 2026 - 9:38

106

Views

how to prove $\|T-T_n\|\le n^{-1/2}$, and is $T$ compact?

Published on 17 Apr 2026 - 11:26

25

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Describe $Z_\circ$, where $Z=J(\{(y_j)\in \ell^\infty:y_{2k}=0\text{ for all $k$ and}\lim_{k\to\infty}y_{2k+1}=0 \})$.

Published on 16 Apr 2026 - 4:59

105

Views

Why does $(a_0I +a_1 T + \dots + a_n T^n ) v = c(T - r_1 I) \dots (T - r_m I) v$ imply that $T - r_j I$ is not injective?

Published on 15 Apr 2026 - 22:55

59

Views

Notion of being Hilbert-Schmidt for multilinear bounded operators

Published on 16 Apr 2026 - 18:42

1.6k

Views

Under what condition is a linear mapping contractive in the sup-norm?

Published on 13 Apr 2026 - 18:14

740

Views

The set of self-adjoint operators over a Hilbert space doesn't form a lattice

Published on 14 Apr 2026 - 15:17

List Question

Describe the bound, range and inverse of a continuous linear transformation

If $X$ is a finite dimensional Hilbert Space, $A$ a bounded operator on $X$, then is $||A||_{op} \leq \rho(A)$?

Is the space of all bounded linear operators a subspace of the space of the linear operators?

Weak-* closed ideal of $L^\infty$

How to show the following operator is linear?

Local linear operator in physical and Fourier space

show that the eigenspace corresponding to every $\lambda_n$ is one dimensional

Is the operator compact or bijective?

Obtaining Hamiltonian Matrix from Operators (Dirac Notation)

how to prove $\|T-T_n\|\le n^{-1/2}$, and is $T$ compact?

Describe $Z_\circ$, where $Z=J(\{(y_j)\in \ell^\infty:y_{2k}=0\text{ for all $k$ and}\lim_{k\to\infty}y_{2k+1}=0 \})$.

Why does $(a_0I +a_1 T + \dots + a_n T^n ) v = c(T - r_1 I) \dots (T - r_m I) v$ imply that $T - r_j I$ is not injective?

Notion of being Hilbert-Schmidt for multilinear bounded operators

Under what condition is a linear mapping contractive in the sup-norm?

The set of self-adjoint operators over a Hilbert space doesn't form a lattice

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