List questions from adjoint-operators

Published on 16 May 2018 - 11:53

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How to prove there is left\right adjoint for non-degenerate bilinear form?

Published on 25 Mar 2026 - 1:17

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Is the kernel of the adjoint operator equal to the kernel of the operator ($\ker (A)=\ker (A')$)?

Published on 21 May 2018 - 18:10

202

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Most general expression for adjoint operators on C2 vector space

Published on 22 May 2018 - 14:05

555

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Spectrum of self-adjoint operator

Published on 23 May 2018 - 12:34

30

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$A$ is bounded if $\displaystyle\lim_{h\to 0}\|e^{ihA}-{\rm id}_\mathcal{H}\|=0$

Published on 25 Mar 2026 - 3:02

73

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If $A$ is a compact operator, then the rank of $A^*A$ is equal to the rank of $A$.

Published on 25 Mar 2026 - 7:45

426

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Self-adjoint operator with increasing sequence of eigenvalues

Published on 28 May 2018 - 14:40

367

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Jordan Normal Form of $T:V\rightarrow V$ if $T^2$ is self adjoint

Published on 25 Mar 2026 - 12:27

244

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Power of $a^{\dagger}=\sqrt{\frac{\omega m }{2 \hbar}}\left (x-\frac{\hbar}{m\omega}\frac{d}{dx} \right)$

Published on 25 Mar 2026 - 11:24

2k

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Proof that every bounded linear operator between hilbert spaces has an adjoint.

Published on 06 Jun 2018 - 2:37

139

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Find the operator norm: $T\in B(L^{2}(\mathbb{R},e^{-x^{2}}dx)) $, $Tf(x) = f(x+1)$. $||T|| = $?

Published on 11 Jun 2018 - 19:13

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Find the adjoint operator $T^*$ of $T:V\to V$ defined by $Tx=x-\frac{2<v,x>}{||v||^2}v$ for some fixed $v\in V$, where $V$ is under $\mathbb{R}$.

Published on 18 Jun 2018 - 23:01

404

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Adjoint conditions in PDEs

Published on 21 Jun 2018 - 16:37

526

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formal adjoint of a vector fields

Published on 22 Jun 2018 - 3:53

List Question

Why is $\langle x,T^*g\rangle=0$?

How to prove there is left\right adjoint for non-degenerate bilinear form?

Is the kernel of the adjoint operator equal to the kernel of the operator ($\ker (A)=\ker (A')$)?

Most general expression for adjoint operators on C2 vector space

Spectrum of self-adjoint operator

$A$ is bounded if $\displaystyle\lim_{h\to 0}\|e^{ihA}-{\rm id}_\mathcal{H}\|=0$

If $A$ is a compact operator, then the rank of $A^*A$ is equal to the rank of $A$.

Self-adjoint operator with increasing sequence of eigenvalues

Jordan Normal Form of $T:V\rightarrow V$ if $T^2$ is self adjoint

Power of $a^{\dagger}=\sqrt{\frac{\omega m }{2 \hbar}}\left (x-\frac{\hbar}{m\omega}\frac{d}{dx} \right)$

Proof that every bounded linear operator between hilbert spaces has an adjoint.

Find the operator norm: $T\in B(L^{2}(\mathbb{R},e^{-x^{2}}dx)) $, $Tf(x) = f(x+1)$. $||T|| = $?

Find the adjoint operator $T^*$ of $T:V\to V$ defined by $Tx=x-\frac{2<v,x>}{||v||^2}v$ for some fixed $v\in V$, where $V$ is under $\mathbb{R}$.

Adjoint conditions in PDEs

formal adjoint of a vector fields

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