List questions from self-adjoint-operators

104

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Why the operator $T$ is positive and self-adjoint, which $(T(t)f)=\sum_{n=0}^{\infty}(n+1)^{-t}c_{n}z^n$?

Published on 28 Apr 2026 - 16:23

253

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Express in terms of $E$ a self-adjoint operator $T$ such that $T^2 = I+E$

Published on 07 May 2026 - 10:18

371

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Showing $(1-x^2)u''-xu'+9u=x^3$ is formally self-adjoint

Published on 28 Apr 2026 - 17:49

262

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Adjoint relation: transpose or conjugate transpose?

Published on 06 May 2026 - 9:24

129

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Dimension of the null space of a compact perturbation of a self-adjoint operator

Published on 28 Apr 2026 - 1:12

274

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Proof of a linear algebra lemma for Cohn-Vossen's theorem

Published on 10 May 2026 - 17:59

375

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Fredholm Alternative for Singular ODE

Published on 28 Apr 2026 - 17:32

415

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Let A be a self-adjoint, compact operator on a Hilbert space. Prove that there are positive operators P and N such that A = P − N and P N = 0.

Published on 06 May 2026 - 7:43

178

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Convergence of (unbounded) self-adjoint operators

Published on 28 Apr 2026 - 12:29

479

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Eigendecomposition of Self-Adjoint Operator with Non-Positive Inner Product

Published on 07 May 2026 - 18:42

59

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If $A+B\ge C$, can we find positive operators $A_1\le A$ and $B_1\le B$ such that $A_1+B_1=C$?

Published on 28 Apr 2026 - 9:58

704

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Find out if a operator is self-adjoint or orthogonal

Published on 10 May 2026 - 16:32

136

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Question about notation for rewriting integral of Laplace Beltrami operator

Published on 10 May 2026 - 16:33

777

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Normal operator with real spectrum is hermitian.

Published on 10 May 2026 - 16:32

38

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Is this statement still true with a weaker condition?

Published on 10 May 2026 - 16:31

List Question

Why the operator $T$ is positive and self-adjoint, which $(T(t)f)=\sum_{n=0}^{\infty}(n+1)^{-t}c_{n}z^n$?

Express in terms of $E$ a self-adjoint operator $T$ such that $T^2 = I+E$

Showing $(1-x^2)u''-xu'+9u=x^3$ is formally self-adjoint

Adjoint relation: transpose or conjugate transpose?

Dimension of the null space of a compact perturbation of a self-adjoint operator

Proof of a linear algebra lemma for Cohn-Vossen's theorem

Fredholm Alternative for Singular ODE

Let A be a self-adjoint, compact operator on a Hilbert space. Prove that there are positive operators P and N such that A = P − N and P N = 0.

Convergence of (unbounded) self-adjoint operators

Eigendecomposition of Self-Adjoint Operator with Non-Positive Inner Product

If $A+B\ge C$, can we find positive operators $A_1\le A$ and $B_1\le B$ such that $A_1+B_1=C$?

Find out if a operator is self-adjoint or orthogonal

Question about notation for rewriting integral of Laplace Beltrami operator

Normal operator with real spectrum is hermitian.

Is this statement still true with a weaker condition?

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