List questions from self-adjoint-operators

Published on 07 May 2026 - 7:51

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Exponential of self-adjoint operator

Published on 27 Mar 2026 - 10:25

62

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Show that the symmetric operator $Sx:=(nx_n)_{n\in\mathbb N}$ on $\mathcal D(S):=\{x\in H:(nx_n)_{n\in\mathbb N}\in\ell^2\}$ is even self-adjoint

Published on 01 May 2026 - 15:56

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If $A$ is self-adjoint, then $\left\|A\right\|=\sup_{x\in H\setminus\{0\}}\frac{\langle Ax,x\rangle}{\left\|x\right\|^2}$

Published on 05 Apr 2026 - 21:26

98

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If $A$ is self-adjoint, then $\left\|A\right\|=\max_{\lambda\in\sigma(A)}|\lambda|$

Published on 25 Mar 2026 - 14:11

431

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Proof of a self-adjoint linear transformation

Published on 25 Mar 2026 - 12:33

608

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An operator that is normal but not self-adjoint

Published on 10 May 2026 - 19:45

1.4k

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Proving a Self-Adjoint Operator is an Orthogonal Projection

Published on 25 Mar 2026 - 12:32

22

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Optimize the contractivity of a self-adjoint operator on a closed subspace

Published on 25 Mar 2026 - 12:37

350

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Does there exist a basis of $\mathbb R^3$ consisting of eigenvectors of T?

Published on 25 Mar 2026 - 12:34

368

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Sum of Shift Operators

Published on 10 May 2026 - 9:53

209

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Bounded self-adjoint linear operator is injective...

Published on 25 Mar 2026 - 12:30

93

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checking if an endomorphism is self-adjoint.

Published on 25 Mar 2026 - 12:30

140

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Show $\sup_{0≤f∈L^2}\frac{\|Af\|_{L^2}}{\|f\|_{L^2}}=\sup_{0≤f∈L^2}\frac{⟨Af,f⟩_{L^2}}{\|f\|_{L^2}^2}$ for self-adjoint nonnegativity-preserving $A$

Published on 25 Mar 2026 - 14:25

29

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What will be the matrix of an anti-selfadjoint transformation in an orthonormal basis?

Published on 25 Mar 2026 - 12:35

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A cyclic vector for the Dirichlet Laplacian on interval.

Exponential of self-adjoint operator

Show that the symmetric operator $Sx:=(nx_n)_{n\in\mathbb N}$ on $\mathcal D(S):=\{x\in H:(nx_n)_{n\in\mathbb N}\in\ell^2\}$ is even self-adjoint

If $A$ is self-adjoint, then $\left\|A\right\|=\sup_{x\in H\setminus\{0\}}\frac{\langle Ax,x\rangle}{\left\|x\right\|^2}$

If $A$ is self-adjoint, then $\left\|A\right\|=\max_{\lambda\in\sigma(A)}|\lambda|$

Proof of a self-adjoint linear transformation

An operator that is normal but not self-adjoint

Proving a Self-Adjoint Operator is an Orthogonal Projection

Optimize the contractivity of a self-adjoint operator on a closed subspace

Does there exist a basis of $\mathbb R^3$ consisting of eigenvectors of T?

Sum of Shift Operators

Bounded self-adjoint linear operator is injective...

checking if an endomorphism is self-adjoint.

Show $\sup_{0≤f∈L^2}\frac{\|Af\|_{L^2}}{\|f\|_{L^2}}=\sup_{0≤f∈L^2}\frac{⟨Af,f⟩_{L^2}}{\|f\|_{L^2}^2}$ for self-adjoint nonnegativity-preserving $A$

What will be the matrix of an anti-selfadjoint transformation in an orthonormal basis?

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