Dirac operators on real spinor bundles of complex type

The Bundles of Algebraic and Dirac-Hestenes Spinor Fields

The main objective of this paper is to clarify the ontology of DiracHestenes spinor fields (DHSF ) and its relationship with even multivector fields, on a Riemann-Cartan spacetime (RCST) M =(M,g,∇, τg, ↑) admitting a spin structure, and to give a mathematically rigorous derivation of the so called Dirac-Hestenes equation (DHE ) in the case where M is a Lorentzian spacetime (the general case whe...

Cartan Spinor Bundles on Manifolds. *

Collapsing and Dirac-type Operators

We analyze the limit of the spectrum of a geometric Dirac-type operator under a collapse with bounded diameter and bounded sectional curvature. In the case of a smooth limit space B, we show that the limit of the spectrum is given by the spectrum of a certain first-order differential operator on B, which can be constructed using superconnections. In the case of a general limit space X , we expr...

Compact composition operators on real Banach spaces of complex-valued bounded Lipschitz functions

We characterize compact composition operators on real Banach spaces of complex-valued bounded Lipschitz functions on metric spaces, not necessarily compact, with Lipschitz involutions and determine their spectra.

Cliiord Structures and Spinor Bundles

It is shown that every bundle ! M of complex, irreducible and faithful modules over the Cliiord bundle of an even-dimensional Riemannian space (M; g) with local model (V; h) is associated with a cpin (\Cliiord") structure on M, this being an extension of the SO(h)-bundle of orthonormal frames on M to the Cliiord group Cpin(h) = (C Spin(h))=Z 2. An explicit construction is given of the total spa...