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Spectral sections

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Abstract

The paper is devoted to the notion of a spectral section introduced by Melrose and Piazza. In the first part of the paper we generalize results of Melrose and Piazza to arbitrary base spaces, not necessarily compact. The second part contains a number of special cases, including cobordism theorems for families of Dirac type operators parametrized by a non-compact base space. In the third part of the paper we investigate whether Riesz continuity is necessary for existence of a spectral section or a generalized spectral section. In particular, we show that if a graph continuous family of regular self-adjoint operators with compact resolvents has a spectral section, then the family is Riesz continuous.

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Acknowledgments

I am grateful to N. V. Ivanov for useful remarks and suggestions.

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Authors and Affiliations

  1. Department of Mathematics, Technion—Israel Institute of Technology, Haifa, 32000, Israel

    Marina Prokhorova

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  1. Marina Prokhorova
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Correspondence to Marina Prokhorova.

Additional information

This work was partially supported by ISF grant no. 431/20.

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Prokhorova, M. Spectral sections. Isr. J. Math. 259, 651–700 (2024). https://doi.org/10.1007/s11856-023-2553-1

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  • DOI: https://doi.org/10.1007/s11856-023-2553-1

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