Question

Infinite-dimensional inner product spaces: if $A^k = I$ for self-adjoint $A$ and for integer $k > 0$, then $A^2 = I$

score 234 · Answer 1 · 2026-03-25 19:05:05

234

Views

Infinite-dimensional inner product spaces: if $A^k = I$ for self-adjoint $A$ and for integer $k > 0$, then $A^2 = I$

Published on 25 Mar 2026 - 19:05

score 54 · Answer 2 · 2026-03-25 19:03:10

54

Views

Prove that $v = 0 \iff v + iT(v) = 0$ for a self adjoint operator

Published on 25 Mar 2026 - 19:03

score 106 · Answer 3 · 2020-06-13 21:22:33

106

Views

Bounded linear operator of $\ell^{2}(\mathbb{N})$ which is normal but not self-adjoint

Published on 13 Jun 2020 - 21:22

score 37 · Answer 4 · 2026-03-25 23:38:31

37

Views

find the hermitian operator of an operator which attaches a matrix and its iverted

Published on 25 Mar 2026 - 23:38

score 44 · Answer 5 · 2026-03-26 01:23:33

44

Views

show that Norm of v+iT(v) equals to the Norm of v-iT(v)

Published on 26 Mar 2026 - 1:23

score 287 · Answer 6 · 2026-03-25 19:04:52

287

Views

Show the operator $I-iT$ is invertible and that $(I-iT)(I+iT)^{-1}$ is unitary operator

Published on 25 Mar 2026 - 19:04

score 1.8k · Answer 7 · 2026-03-25 19:02:33

1.8k

Views

prove that an operator is unitary

Published on 25 Mar 2026 - 19:02

score 469 · Answer 8 · 2020-06-22 20:49:08

469

Views

Adjoint operator for $l^2(\mathbb{N})$

Published on 22 Jun 2020 - 20:49

score 318 · Answer 9 · 2026-03-25 22:05:19

318

Views

Infinite-dimensional inner product space: if $A \geq 0$ and if $\langle Ax, x\rangle = 0$ for some $x$, then $Ax = 0$.

Published on 25 Mar 2026 - 22:05

score 108 · Answer 10 · 2020-06-25 02:09:50

108

Views

Positivity of an eigenvalue of a composition of a differential operator and its formal adjoint

Published on 25 Jun 2020 - 2:09

score 193 · Answer 11 · 2026-03-26 04:59:38

193

Views

a linear map on $W$

Published on 26 Mar 2026 - 4:59

score 682 · Answer 12 · 2020-07-10 01:00:27

682

Views

Prove that a positive operator is invertible

Published on 10 Jul 2020 - 1:00

score 62 · Answer 13 · 2026-03-25 19:10:08

62

Views

Define a linear functional $T$ on $V$ by $Tv$ = $\langle v, u\rangle$. What is $T^∗ (\alpha)$ for a scalar $\alpha$ where $T^*$ is the adjoint.

Published on 25 Mar 2026 - 19:10

score 71 · Answer 14 · 2020-07-21 13:37:38

71

Views

If $T\colon X \to Y$ is such that $T^\colon Y^ \to Y^*$, what does this imply about $T$?

Published on 21 Jul 2020 - 13:37

score 68 · Answer 15 · 2020-07-22 18:50:52

68

Views

Let $T=\int_{0}^{x}f(y)dt$. Find eigenvalues and range of $T+T^*$

Published on 22 Jul 2020 - 18:50

List Question

Infinite-dimensional inner product spaces: if $A^k = I$ for self-adjoint $A$ and for integer $k > 0$, then $A^2 = I$

Prove that $v = 0 \iff v + iT(v) = 0$ for a self adjoint operator

Bounded linear operator of $\ell^{2}(\mathbb{N})$ which is normal but not self-adjoint

find the hermitian operator of an operator which attaches a matrix and its iverted

show that Norm of v+iT(v) equals to the Norm of v-iT(v)

Show the operator $I-iT$ is invertible and that $(I-iT)(I+iT)^{-1}$ is unitary operator

prove that an operator is unitary

Adjoint operator for $l^2(\mathbb{N})$

Infinite-dimensional inner product space: if $A \geq 0$ and if $\langle Ax, x\rangle = 0$ for some $x$, then $Ax = 0$.

Positivity of an eigenvalue of a composition of a differential operator and its formal adjoint

a linear map on $W$

Prove that a positive operator is invertible

Define a linear functional $T$ on $V$ by $Tv$ = $\langle v, u\rangle$. What is $T^∗ (\alpha)$ for a scalar $\alpha$ where $T^*$ is the adjoint.

If $T\colon X \to Y$ is such that $T^\colon Y^ \to Y^*$, what does this imply about $T$?

Let $T=\int_{0}^{x}f(y)dt$. Find eigenvalues and range of $T+T^*$

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