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On the Nejfeld-connection in the Grassmann manifold of Banach type. (Russian) Zbl 0728.58003
It is regarded the Grassmannian manifold $$G_{F,M}(E)$$ of all closed subspaces of the Banach space E which are isomorphic to the space F and permit topological additions isomorphic to the space M. Any morphism $${\mathcal N}: G_{F,M}(E)\to G_{M,F}(E)$$ with property $$\forall F_ 0\subset G_{F,M}(E):F_ 0\oplus {\mathcal N}(F_ 0)=E$$ gives the linear connection of Nejfeld. With the help of the projection-method of Egiazaryan the operator of this linear connection, that is generalizing the n-dimensional case, is found.
##### MSC:
 58B05 Homotopy and topological questions for infinite-dimensional manifolds
##### Keywords:
Grassmannian manifold; Banach space; linear connection
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