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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 Fredholm realizations of semi-Fredholm operators in a Hilbert space. Such a realization is determined by an abstract boundary condition, which is a subspace of the space of abstract boundary values. We find the $K^0$ index of a family of Fredholm realizations of semi-Fredholm operators in terms of the corresponding family of boundary conditions. Similarly, we find the $K^1$ index of a family of self-adjoint Fredholm extensions of symmetric semi-Fredholm operators. 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. 2024-01-29. Family index for Fredholm extensions of semi-Fredholm operators. https://arxiv.org/abs/2401.16060

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