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arXiv · 2401.16060

Family index for Fredholm extensions of semi-Fredholm operators

Marina Prokhorova
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Abstract

This paper is devoted to an abstract analogue of elliptic boundary value problems, namely, Fredholm realizations of semi-Fredholm operators in a Hilbert space. Such a realization is determined by an abstract boundary condition, which is a subspace in the space of abstract boundary values. We find the $K^0$ index of a family of such abstract boundary value problems, or the $K^1$ index in the self-adjoint case, in terms of the corresponding family of abstract boundary conditions. Our approach is based on passing from a Fredholm operator to its graph. The graph forms a Fredholm pair with the horizontal subspace, and we prove the index formula by deforming the horizontal subspace instead of the operator.

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Marina Prokhorova. 2026-09-14. Family index for Fredholm extensions of semi-Fredholm operators. https://arxiv.org/abs/2401.16060

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