DIFFERENTIABLE BUNDLES OF SUBSPACES AND OPERATORS IN BANACH-SPACES

This paper follows the line of ideas of R. Janz [3], [4] who introduced a notion of continuous and holomorphic bundles of subspaces of a Banach space. His concepts constitute an elegant framework for the study of unbounded operators which depend on a parameter. Motivated by the work of Janz we investigate bundles of closed linear subspaces of a Banach space which are differentiable in a suitable sense. Our construction is based on lifting results for differentiable functions which have been established by the author in [6], [7].