Family index for Fredholm extensions of semi-Fredholm operators

Autor:	Prokhorova, Marina
Rok vydání:	2024
Předmět:	Mathematics - Differential Geometry Mathematics - Functional Analysis
Druh dokumentu:	Working Paper
Popis:	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. Comment: 36 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2401.16060 Zobrazit plný text záznamu View this record from Arxiv