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The geometry of Kato Grassmannians |
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| Authors: | Bojarski Bogdan Khimshiashvili Giorgi |
| Affiliation: | (1) Institute of Mathematics, Polish Academy of Sciences, Sniadeckich str. 8, Warsaw, Poland;(2) A. Razmadze Mathematical Institute, Georgian Academy of Sciences, M. Aleksidze str. 1, 0193 Tbilisi, Georgia |
| Abstract: | We discuss Fredholm pairs of subspaces and associated Grassmannians in a Hilbert space. Relations between several existing definitions of Fredholm pairs are established as well as some basic geometric properties of the Kato Grassmannian. It is also shown that the so-called restricted Grassmannian can be endowed with a natural Fredholm structure making it into a Fredholm Hilbert manifold. |
| Keywords: | Fredholm pair of subspaces Fredholm operator index compact operator restricted Grassmannian Hilbert manifold homotopy groups Fredholm structure |
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