List questions from adjoint-operators

Published on 10 Apr 2018 - 7:00

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If H is Hermitian, show that $e^{iH}$ is unitary

Published on 25 Mar 2026 - 14:12

58

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How do I find adjoint operator in different bases?

Published on 10 Apr 2018 - 20:10

183

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Domains of higher powers of two unbounded self-adjoint operators

Published on 12 Apr 2018 - 3:43

125

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Prove bounded linear operator equal 0

Published on 16 Apr 2018 - 22:13

186

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Prove it is possible $Tv =\lambda v$ while v is not an eigenvector of T* with eigenvalue $\overline{\lambda}$.

Published on 20 Apr 2018 - 21:04

181

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Is $I-2T$ self-adjoint for a rank-one operator $\,Tx=\langle\,x\mid u\,\rangle u\,$ on Hilbert space with $\|u\|=1$?

Published on 22 Apr 2018 - 20:20

2.5k

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Show that $U$ is a unitary operator if and only if $[U]_{\mathcal{B}}$ is a unitary matrix.

Published on 23 Apr 2018 - 6:16

940

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Residual spectrum of the adjoint on Banach space

Published on 25 Mar 2026 - 14:26

63

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The ranges of $T+iI$ and of $T-iI$.

Published on 25 Mar 2026 - 6:29

148

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Show that the integral-operator compact?

Published on 25 Mar 2026 - 7:47

128

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Boundary conditions for self-adjoint linear diffrential operators

Published on 25 Mar 2026 - 16:06

2.3k

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prove that $\lambda$ is eigenvalue of $T$ if and only if $\bar{\lambda}$ is eigenvalue for $T^*$

Published on 03 May 2018 - 3:33

467

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Find the eigenvalues and eigenfunctions of the operator

Published on 25 Mar 2026 - 7:58

97

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Understanding $\overline{Im\: }A=\bigcap_{A'f=0}\ker f$ proof

Published on 15 May 2018 - 15:49

List Question

Calculate Adjoint of an operator with a non-standard inner product.

If H is Hermitian, show that $e^{iH}$ is unitary

How do I find adjoint operator in different bases?

Domains of higher powers of two unbounded self-adjoint operators

Prove bounded linear operator equal 0

Prove it is possible $Tv =\lambda v$ while v is not an eigenvector of T* with eigenvalue $\overline{\lambda}$.

Is $I-2T$ self-adjoint for a rank-one operator $\,Tx=\langle\,x\mid u\,\rangle u\,$ on Hilbert space with $\|u\|=1$?

Show that $U$ is a unitary operator if and only if $[U]_{\mathcal{B}}$ is a unitary matrix.

Residual spectrum of the adjoint on Banach space

The ranges of $T+iI$ and of $T-iI$.

Show that the integral-operator compact?

Boundary conditions for self-adjoint linear diffrential operators

prove that $\lambda$ is eigenvalue of $T$ if and only if $\bar{\lambda}$ is eigenvalue for $T^*$

Find the eigenvalues and eigenfunctions of the operator

Understanding $\overline{Im\: }A=\bigcap_{A'f=0}\ker f$ proof

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