# Tagged Questions

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### Spectrum of an operator from Transpose sum

I was wondering if there is anything we can know about the spectrum of an operator $A$ if we know that $M = A + A^{T}$ is a positive operator?
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### Perturbation of spectrum and eigenspaces

Let $A \in \mathbb{C}^{n \times n}$ be an $n \times n$ matrix. Consider the rank-$1$ perturbation $A'$ of $A$ given by replacing a column $v$ of $A$ by $\alpha \cdot v$, where $\alpha \in [0, 1)$. Can ...
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### A version of the spectral theorem for group actions

Suppose $G$ is a sufficiently nice (maybe locally compact and abelian) group which acts on the separable Hilbert space $\mathcal{H}$ by unitary transformations. Is there a generalization of the ...
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### Versions of the spectral theorem

Since any $C^*$-algebra can be represented as an algebra of bounded operators $\mathcal{B(H)}$ on a Hilbert space $\mathcal{H}$, the spectral theorem applies to all $C^*$-algebras: ($*$) ...
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### A.C. spectrum of the non additive perturbation BAB of a self-adjoint operator A where B is strictly positive

If have the following problem: Let $A : \mathcal{H} \to \mathcal{H}$ be a bounded, self-adjoint operator on some Hilbert space $\mathcal{H}$. Let $B: \mathcal{H} \to \mathcal{H}$ be a bounded, ...
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### A doubt about the parts of the spectrum of tensor products

Let $\mathcal{H}$ be any complex Hilbert space of infinite dimensional. By an operator $T$ I mean a linear bounded transformation from $\mathcal{H}$ into $\mathcal{H}$, i.e, ...
Let $\rho(M)$ denote the spectral radius (modulus of the largest eigenvalue) of a square matrix $M$. I am looking for a characterization or anything else interesting about the set of matrices $A$ ...
As we know, continuous spectrum and residual spectrum are two cases in the spectrum of an operator, which only appear in infinite dimension. If $T$ is a operator from Banach space $X$ to $X$, $aI-T$ ...