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Characterizations of open multivalued linear operators

Author:
Álvarez Seco, María TeresaUniovi authority
Publication date:
2006
Editorial:

Polish Academy of Sciences, Institute of Mathematics

Publisher version:
http://dx.doi.org/10.4064/sm175-3-1
Citación:
Studia Mathematica, 175, 205-212 (2006); doi:10.4064/sm175-3-1
Descripción física:
p. 205-2012
Abstract:

The class of all open linear relations is characterised in terms of the re- strictions of the linear relations to finite-codimensional subspaces. As an application, we establish two results, the first of which shows that an upper semi-Fredholm linear relation retains its index under finite rank perturbations, and the second is a density theorem for lower bounded linear relations that have closed range. Results of Labuschagne and of Mbekhta about linear operators are covered.

The class of all open linear relations is characterised in terms of the re- strictions of the linear relations to finite-codimensional subspaces. As an application, we establish two results, the first of which shows that an upper semi-Fredholm linear relation retains its index under finite rank perturbations, and the second is a density theorem for lower bounded linear relations that have closed range. Results of Labuschagne and of Mbekhta about linear operators are covered.

URI:
http://hdl.handle.net/10651/8394
ISSN:
0039-3223; 1730-6337
DOI:
10.4064/sm175-3-1
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