Translator Disclaimer
June 1998 The Maslov Index: a Functional Analytical Definition and the Spectral Flow Formula
Bernhelm BOOSS-BAVNBEK, Kenro FURUTANI
Tokyo J. Math. 21(1): 1-34 (June 1998). DOI: 10.3836/tjm/1270041982

Abstract

We give a functional analytical definition of the Maslov index for continuous curves in the Fredholm-Lagrangian Grassmannian. Our definition does not require assumptions either at the endpoints or at the crossings of the curve with the Maslov cycle. We demonstrate an application of our definition by developing the symplectic geometry of self-adjoint extensions of unbounded symmetric operators. We discuss continuous variations of the form $A_D+C_t$, where $A_D$ is a fixed self-adjoint unbounded Fredholm operator and $\{C_t\}$ a family of bounded self-adjoint operators. We extend the definition of the spectral flow to such families of unbounded operators in a purely functional analytical way. We then prove that the spectral flow is equal to the Maslov index of the corresponding family of abstract Cauchy data spaces.

Citation

Download Citation

Bernhelm BOOSS-BAVNBEK. Kenro FURUTANI. "The Maslov Index: a Functional Analytical Definition and the Spectral Flow Formula." Tokyo J. Math. 21 (1) 1 - 34, June 1998. https://doi.org/10.3836/tjm/1270041982

Information

Published: June 1998
First available in Project Euclid: 31 March 2010

zbMATH: 0932.37063
MathSciNet: MR1630119
Digital Object Identifier: 10.3836/tjm/1270041982

Rights: Copyright © 1998 Publication Committee for the Tokyo Journal of Mathematics

JOURNAL ARTICLE
34 PAGES


SHARE
Vol.21 • No. 1 • June 1998
Back to Top