Question

Show that if $T$ is an invertible bounded linear operator on $\ell^2 (\mathbb{N})$, then $\|S − T\| \geq 1$

score 92 · Answer 1 · 2026-04-15 03:56:05

92

Views

Show that if $T$ is an invertible bounded linear operator on $\ell^2 (\mathbb{N})$, then $\|S − T\| \geq 1$

Published on 15 Apr 2026 - 3:56

score 81 · Answer 2 · 2026-04-15 21:41:55

81

Views

Show that there is no operator $T \in L(\ell^2(\mathbb{N}))$

Published on 15 Apr 2026 - 21:41

score 77 · Answer 3 · 2026-04-14 10:07:34

77

Views

Compute $\|(iI + \frac{1}{2}U)^{-1}\|$

Published on 14 Apr 2026 - 10:07

score 63 · Answer 4 · 2026-04-12 07:24:08

63

Views

Conclude operator convergence from convergence of the eigenspaces

Published on 12 Apr 2026 - 7:24

score 260 · Answer 5 · 2026-04-12 20:01:55

260

Views

Spectrum of restriction to invariant subspace

Published on 12 Apr 2026 - 20:01

score 124 · Answer 6 · 2026-04-11 18:05:34

124

Views

Which linear operator has a spectrum that corresponds to the physical light spectrum?

Published on 11 Apr 2026 - 18:05

score 239 · Answer 7 · 2026-04-11 13:03:49

239

Views

Weak and strong convergence of a sequence of operators in $L^2(\mathbb{R})$

Published on 11 Apr 2026 - 13:03

score 295 · Answer 8 · 2026-04-14 17:39:05

295

Views

Higher derivatives of the map $I:T \mapsto T^{-1}$, where $T \in \mathcal B(X)$.

Published on 14 Apr 2026 - 17:39

score 82 · Answer 9 · 2026-04-10 18:09:28

82

Views

Infinite-dimensional inner product spaces: if $A$ is a skew operator, does it follow that $A-I$ is invertible?

Published on 10 Apr 2026 - 18:09

score 61 · Answer 10 · 2026-03-26 01:29:10

61

Views

What can we infer from a growth bound What can we infer from the condition $\limsup_{n\to\infty}\frac{\ln\left\|A_n\right\|}n\le0$?

Published on 26 Mar 2026 - 1:29

score 175 · Answer 11 · 2026-04-11 19:11:25

175

Views

Eigenvalues of the fractional power of a compact operator

Published on 11 Apr 2026 - 19:11

score 52 · Answer 12 · 2026-03-25 12:28:13

52

Views

Find a Borel measure $\mu$ such that $\int_0^1 f(t) d\mu(t)=\Lambda f, \forall f\in C[0,1]$

Published on 25 Mar 2026 - 12:28

score 169 · Answer 13 · 2026-03-25 17:38:37

169

Views

$f(t) = \min\{1,t\}$ not operator monotone

Published on 25 Mar 2026 - 17:38

score 47 · Answer 14 · 2026-04-16 05:48:44

47

Views

What conditions on $p$ and $q$ to for which the operator $T_g: L^p([0,1]) \to L^q([0,1])$ is bounded, where $T_g(f)=gf$

Published on 16 Apr 2026 - 5:48

score 46 · Answer 15 · 2026-04-14 19:56:19

46

Views

Local uniqueness in nonlinear ODE

Published on 14 Apr 2026 - 19:56

List Question

Show that if $T$ is an invertible bounded linear operator on $\ell^2 (\mathbb{N})$, then $\|S − T\| \geq 1$

Show that there is no operator $T \in L(\ell^2(\mathbb{N}))$

Compute $\|(iI + \frac{1}{2}U)^{-1}\|$

Conclude operator convergence from convergence of the eigenspaces

Spectrum of restriction to invariant subspace

Which linear operator has a spectrum that corresponds to the physical light spectrum?

Weak and strong convergence of a sequence of operators in $L^2(\mathbb{R})$

Higher derivatives of the map $I:T \mapsto T^{-1}$, where $T \in \mathcal B(X)$.

Infinite-dimensional inner product spaces: if $A$ is a skew operator, does it follow that $A-I$ is invertible?

What can we infer from a growth bound What can we infer from the condition $\limsup_{n\to\infty}\frac{\ln\left\|A_n\right\|}n\le0$?

Eigenvalues of the fractional power of a compact operator

Find a Borel measure $\mu$ such that $\int_0^1 f(t) d\mu(t)=\Lambda f, \forall f\in C[0,1]$

$f(t) = \min\{1,t\}$ not operator monotone

What conditions on $p$ and $q$ to for which the operator $T_g: L^p([0,1]) \to L^q([0,1])$ is bounded, where $T_g(f)=gf$

Local uniqueness in nonlinear ODE

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