# Tagged Questions

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### In which cases the spectrum of an operator contains only eigenvalues?

Let $X\neq \{0\}$ be a complex normed spaces (not necessarily finite-dimensional) and $T:D(T)\subset X\to X$ a linear operator (not necessarily bounded). I would like to know under what conditions can ...
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### Spectral Mapping Theorem

Spectral mapping theorem is as follows: https://math.uc.edu/~halpern/Matrix.methods/Homatrixmethods/Spectralmappingthm.pdf Is Spectral mapping theorem true for point spectrum ?
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### Resolvent R(1) of the Laplace operator not compact

I want to show that $$R_\Delta(1):=(1-\Delta)^{-1}$$ is not compact in $\mathbb{R}^3$. I have found that for $\chi_{B}$ being the characteristic function for a set $B\subset\mathbb{R}^n$, ...
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### Spectrum of operator

Like my previous question, I'm considering the same space and operator: Hilbertspace adjoint But this time I am trying to determine the spectrum of $T$. I feel like I'm messing up my definitions a ...
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### spectum of self adjoint operators

Let $H$ be an Hilbert space and $S = \displaystyle{ \sum_{i=1}^nS_i}$ where $S_i$ (i=1...n) is self adjoint with compact resolvent . is it true that the spectrum of $S$ is the sum of the spectra of ...
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### $T\in B(H)$ normal and left invertible implies $T$ invertible?

My question is what's written in the title, that is, if $T$ is a normal operator on a Hilbert space $H$, and $T$ is left invertible, is it necessarily true that $T$ is invertible? Actually, the more ...
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