# Geometric properties of Dirichlet forms under order isomorphisms

@article{Lenz2018GeometricPO, title={Geometric properties of Dirichlet forms under order isomorphisms}, author={D. Lenz and M. Schmidt and Melchior Wirth}, journal={arXiv: Functional Analysis}, year={2018} }

We study pairs of Dirichlet forms related by an intertwining order isomorphisms between the associated $L^2$-spaces. We consider the measurable, the topological and the geometric setting respectively. In the measurable setting, we deal with arbitrary (irreducible) Dirichlet forms and show that any intertwining order isomorphism is necessarily unitary (up to a constant). In the topological setting we deal with quasi-regular forms and show that any intertwining order isomorphism induces a quasi… Expand

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#### References

SHOWING 1-10 OF 49 REFERENCES

Intertwining, Excursion Theory and Krein Theory of Strings for Non-self-adjoint Markov Semigroups

- Mathematics
- 2017

Intrinsic metrics for non-local symmetric Dirichlet forms and applications to spectral theory

- Mathematics
- 2010

Analysis on local Dirichlet spaces. I. Recurrence, conservativeness and Lp-Liouville properties.

- Mathematics
- 1994

EIGENVALUES OF THE LAPLACE OPERATOR ON CERTAIN MANIFOLDS.

- Mathematics, Medicine
- Proceedings of the National Academy of Sciences of the United States of America
- 1964