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.
@article{bwmeta1.element.doi-10_2478_BF02475627,
author = {Bogdan Bojarski and Giorgi Khimshiashvili},
title = {The geometry of Kato Grassmannians},
journal = {Open Mathematics},
volume = {3},
year = {2005},
pages = {705-717},
zbl = {1122.58005},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_BF02475627}
}
Bogdan Bojarski; Giorgi Khimshiashvili. The geometry of Kato Grassmannians. Open Mathematics, Tome 3 (2005) pp. 705-717. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_BF02475627/
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