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Abstract
Given a complex Banach algebra, we consider the Stiefel bundle relative to the similarity class of a fixed projection. In the holomorphic category the Stiefel bundle is a holomorphic locally trivial principal bundle over a certain Grassmann manifold. Our main application concerns the holomorphic parametrization of framings for projections. In the spatial case this amounts to a holomorphic parametrization of framings for a corresponding complex Banach space.
Key words and phrases:: Banach algebra; projections; Stiefel bundle; Grassmannian; Banach homogeneous space
Received: 2001-09-17
Published Online: 2010-02-24
Published in Print: 2002-September
© Heldermann Verlag