List questions from self-adjoint-operators

Published on 02 Nov 2017 - 8:46

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Is every self-adjoint operator bounded?

Published on 12 Jan 2018 - 16:30

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Show $e^{-tA}$ is a trace class operator, $t>0$

Published on 23 Mar 2026 - 22:08

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An exponent operator affiliated to a vN algebra.

Published on 24 Mar 2026 - 11:55

39

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Result of $\int_0^1 Tr(e^{-a(1-t)T}A^{∗}e^{-atT}B)) dt , a>0$

Published on 24 Mar 2026 - 5:16

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Let $T:V\to V$ be a linear map, where $V$ is an inner product space. Given $T^2=\frac{T+T^*}{2}$, prove that $T$ is normal and that $T=T^2$.

Published on 10 Aug 2020 - 11:08

105

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Countability of the set of $t$ such that $E-tB$ is not injective

Published on 24 Mar 2026 - 12:01

417

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Solve the ODE $(x-1)y'' - xy' + y = 1$ subject to boundary conditions $y(0)=0,y(1)=2$ using Greens function

Published on 24 Mar 2026 - 0:05

285

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If $A$ and $B$ are self-adjoint and positive operators show that also their product $C=AB$ is self-adjoint and positive

Published on 21 Aug 2020 - 12:20

62

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how to get the following inequality $\|S_nx − S_mx\|_{H}^2 \leq 2M(S_mx −S_nx, x)$?

Published on 23 Mar 2026 - 18:12

331

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Self-adjoint bounded operator with finite spectrum implies diagonalisable?

Published on 24 Mar 2026 - 12:54

164

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If $A$ is a self-adjoint operator then $(A(u),u) \geq 0$?

Published on 24 Mar 2026 - 8:35

158

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How prove that the square root operator commutes with every operator $X$ that commutes with its square

Published on 24 Mar 2026 - 8:34

233

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Finding positive semi-definite counterexamples for self-adjoint bounded operators on a Hilbert Space.

Published on 23 Mar 2026 - 23:16

37

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How do I show complex symmetry properly?

Published on 24 Mar 2026 - 14:47

List Question

Show that $x$ is an eigenvector of $T$ with eigenvalue $\|T\|$

Is every self-adjoint operator bounded?

Show $e^{-tA}$ is a trace class operator, $t>0$

An exponent operator affiliated to a vN algebra.

Result of $\int_0^1 Tr(e^{-a(1-t)T}A^{∗}e^{-atT}B)) dt , a>0$

Let $T:V\to V$ be a linear map, where $V$ is an inner product space. Given $T^2=\frac{T+T^*}{2}$, prove that $T$ is normal and that $T=T^2$.

Countability of the set of $t$ such that $E-tB$ is not injective

Solve the ODE $(x-1)y'' - xy' + y = 1$ subject to boundary conditions $y(0)=0,y(1)=2$ using Greens function

If $A$ and $B$ are self-adjoint and positive operators show that also their product $C=AB$ is self-adjoint and positive

how to get the following inequality $\|S_nx − S_mx\|_{H}^2 \leq 2M(S_mx −S_nx, x)$?

Self-adjoint bounded operator with finite spectrum implies diagonalisable?

If $A$ is a self-adjoint operator then $(A(u),u) \geq 0$?

How prove that the square root operator commutes with every operator $X$ that commutes with its square

Finding positive semi-definite counterexamples for self-adjoint bounded operators on a Hilbert Space.

How do I show complex symmetry properly?

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