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- W2051175069 abstract "First we discuss some difficulties with the currently available definitions of spectral flow (SF). Then we use the Cayley transform to study the topology of the space CFsa (H) of (generally unbounded) self-adjoint Fredholm operators in a fixed complex separable Hilbert space H and give two different (but equivalent) rigorous definitions of SF as a homotopy invariant for continuous paths in CFsa (H). Our study is based on the gap (= projection or graph norm) topology. As examples, we consider families of operators of Dirac type on a compact manifold M with boundary, acting on sections of a fixed Hermitian vector bundle E with domains defined by varying global well-posed boundary conditions. Such families are continuous families in CFsa (L2(M;E)) if the coefficients of the Dirac operators and the boundary conditions vary continuously. No additional assumptions are required." @default.
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- W2051175069 date "2002-01-01" @default.
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- W2051175069 title "Spectral flow of paths of self-adjoint Fredholm operators" @default.
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- W2051175069 doi "https://doi.org/10.1016/s0920-5632(01)01608-5" @default.
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