Abstract
In this paper, we define an analytical index for a continuous family of Fredholm operators parameterized by a topological space \({\mathbb {X}}\) into a Hilbert space H, as a sequence of integers, extending naturally the usual definition of the index and we prove the homotopy invariance of the index. We give also an extension of the Weyl theorem for normal continuous families and we prove that if H is separable, then the space of B-Fredholm operators on H is path connected.
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The author would like to thank the referee for his comments, which led to an important improvement of Theorem 2.15.
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Berkani, M. A new approach in index theory. Math. Z. 298, 943–951 (2021). https://doi.org/10.1007/s00209-020-02640-3
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DOI: https://doi.org/10.1007/s00209-020-02640-3