# Tagged Questions

Spectral theory is the study of generalized notions of eigenvalues and eigenvectors for linear operators in Banach spaces.

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### Article in spectral theory

Can someone please help me to understand how we prove the first inequality (Page 7) in this article http://arxiv.org/pdf/1510.01567.pdf It seems that we use the Young inequality but i didn't know ...
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### Existence of minimal projection in a sub-algebra of compact operators

I am not sure that I explained to myself the missing details in the proof right, so please check my explanations. (The proof is taken from "$C^*$ -Algebras by Example"-Davidson) First, I don't know ...
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### Two formula for an operator

we define the operator P with domain $C_0^\infty(R^{2n})$ by $P=y.\partial _x -\partial _x V(x).\partial_y-\Delta_y+\frac{|y|^2}{4}-\frac{n}{2}$ I want to prove that $P=X_0 +\sum _{i=1}{^n}X_j^*X_j$ ...
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Doesn't the the Mercer's theorem say something stronger than just the spectral theory of compact self-adjoint operators on a Hilbert space applied to the reproducing "kernel" function? As in if I ...
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### Minimum of the Spectrum for a Closed Operator

If $T$ is closed is it true that if $\lambda=\min\{\sigma(T)\}$ and $((T-\lambda)f,f))=0$ then $(T-\lambda)f=0$? This is for a fixed $f\in\mathscr{H}$.
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### Fokker Planck operator is accretive

I would like to show that the Fokker Planck operator with domain $C_0^\infty \left(R^{2n}\right)$ defined by $$K= v.∂_x − (∂_xV (x)).∂_v + (−∂_v +v/2).(∂_v +v/2)$$ is essentially maximal accretive ...
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### Uniqueness of positive square root of postive element in C* algebra

If a is a positive element then it has a unique positive square root, i.e. a unique b positive such that b^2=a. I understand the existence part of the proof. If ...