Defines analytic index for Clifford anti-linear, skew-adjoint, self-adjoint and odd Fredholm operators on real Hilbert C*-modules and proves a real Robbin-Salamon theorem linking spectral flow to Fredholm index via Van Daele K-theory.
On the noncommutative spectral flow
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abstract
We define and study the noncommutative spectral flow for paths of regular selfadjoint Fredholm operators on a countably generated Hilbert C*-module. We give an axiomatic description and discuss some applications. One of them is the definition of a noncommutative Maslov index for paths of Lagrangians which appears in a splitting formula for the spectral flow. Analogously we study the spectral flow for odd operators on a graded module.
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math.OA 1years
2026 1verdicts
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Analytic index theory and spectral flow in real Hilbert $C^*$-modules
Defines analytic index for Clifford anti-linear, skew-adjoint, self-adjoint and odd Fredholm operators on real Hilbert C*-modules and proves a real Robbin-Salamon theorem linking spectral flow to Fredholm index via Van Daele K-theory.