Friday, May 25, 2018 - 16:15 in V3-204
The numerical range of positive operators
A talk in the Kolloquium Mathematische Physik series by
Agnes Radl from Greifswald
| Abstract: |
The numerical range of a linear operator $A$ on a Hilbert space $H$ is defined as $W(A):=\{\langle Ax, x \rangle \colon x \in H, \|x\| = 1 \}$. It is well-known that the closure of the numerical range contains the spectrum. Hence, it can be used to localise the spectrum. In this talk, we will first study symmetry properties of the numerical range of positive operators in Hilbert lattices. Then, we will investigate various generalisations of the numerical range. It turns out that the numerical range exhibits a certain rotational symmetry which is similar to the rotational symmetry of the spectrum of a positive operator.
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