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Bibliographic Details
Main Author:	Prokhorova, Marina
Format:	Preprint
Published:	2024
Subjects:	Differential Geometry Functional Analysis
Online Access:	https://arxiv.org/abs/2401.16060
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author	Prokhorova, Marina
author_facet	Prokhorova, Marina
contents	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.
format	Preprint
id	arxiv_https___arxiv_org_abs_2401_16060
institution	arXiv
publishDate	2024
record_format	arxiv
spellingShingle	Family index for Fredholm extensions of semi-Fredholm operators Prokhorova, Marina Differential Geometry Functional Analysis 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.
title	Family index for Fredholm extensions of semi-Fredholm operators
topic	Differential Geometry Functional Analysis
url	https://arxiv.org/abs/2401.16060

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