Family index for Fredholm extensions of semi-Fredholm operators
Autor: | Prokhorova, Marina |
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Rok vydání: | 2024 |
Předmět: | |
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 |
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