Bernhelm Booss

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We study the gap (= " projection norm " = " graph norm ") topology of the space of (not necessarily bounded) self–adjoint Fredholm operators in a separable Hilbert space by the Cayley transform and direct methods. In particular, we show that the space is connected contrary to the bounded case. Moreover, we present a rigorous definition of spectral flow of a(More)
We consider a continuous curve of self-adjoint Fred-holm extensions of a curve of closed symmetric operators with fixed minimal domain D m and fixed intermediate domain D W. Our main example is a family of symmetric generalized operators of Dirac type on a compact manifold with boundary with varying well-posed boundary conditions. Here D W is the first(More)
We consider a continuous curve of linear elliptic formally self-adjoint differential operators of first order with smooth coefficients over a compact Riemannian manifold with boundary together with a continuous curve of global elliptic boundary value problems. We express the spectral flow of the resulting continuous family of (unbounded) self-adjoint(More)
We review the concepts of the index of a Fredholm operator, the spectral flow of a curve of self-adjoint Fredholm operators, the Maslov index of a curve of Lagrangian subspaces in symplectic Hilbert space, and the eta invariant of operators of Dirac type on closed manifolds and manifolds with boundary. We emphasize various (occasionally overlooked) aspects(More)
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