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On a new topology in the space of Fredholm operators

โœ Scribed by Anvar Irmatov

Publisher
Springer
Year
1989
Tongue
English
Weight
604 KB
Volume
7
Category
Article
ISSN
0232-704X

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โœฆ Synopsis

In this paper the F-topology is introduced in the space of Fredholm operators F(1 2 (C)). As a subbase of this topology the following sets are considered:

Here Vdenotes a subspace of the Hilbert space 1 2 (C), dim V < o, a, ... , a, e 1 2 (C), and GL(1 2 (C)) denotes the group of invertible operators. Connections of this topology with other possible topologies are investigated. In one of the theorems it is proved that the identity map from the space of Fredholm operators, provided with the uniform topology, to the same space, provided with the F-topology, is a homotopy equivalence.

๐Ÿ“œ SIMILAR VOLUMES

On the Topology of the Space of Hankel C
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โœ J.J. Betancor; I. Marrero ๐Ÿ“‚ Article ๐Ÿ“… 1996 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 145 KB

its space of convolution operators, and let O O be the predual of O O X . We prove , เ ป , เ ป that the topology of uniform convergence on bounded subsets of H H and the strong dual toplogy coincide on O O X . Our technique, involving Mackey topologies, differs , เ ป from, and is simpler than, those usual