To each path of self-adjoint Fredholm operators acting on a real separable Hilbert space H with invertible ends, there is associated an integer called spectral flow. The purpose of this brief note is to show that spectral flow is uniquely characterized by four elementary properties: normalization, continuity, additivity over direct sums, and its value as the difference of the Morse indices of the ends when H is finite dimensional. The proof of uniqueness relies of the invarianceof spectral flow of the path under cogredient transformations of the path.

Uniqueness of spectral flow / Ciriza, E.; Fitzpatrick, P. M.; Pejsachowicz, Jacobo. - In: MATHEMATICAL AND COMPUTER MODELLING. - ISSN 0895-7177. - STAMPA. - 32:11-13(2000), pp. 1495-1501.

### Uniqueness of spectral flow

#### Abstract

To each path of self-adjoint Fredholm operators acting on a real separable Hilbert space H with invertible ends, there is associated an integer called spectral flow. The purpose of this brief note is to show that spectral flow is uniquely characterized by four elementary properties: normalization, continuity, additivity over direct sums, and its value as the difference of the Morse indices of the ends when H is finite dimensional. The proof of uniqueness relies of the invarianceof spectral flow of the path under cogredient transformations of the path.
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Utilizza questo identificativo per citare o creare un link a questo documento: `http://hdl.handle.net/11583/2499049`