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The class of all open linear relations is characterised in terms of the restrictions 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.
T. Álvarez. "Characterisations of open multivalued linear operators." Studia Mathematica 175.3 (2006): 205-212. <http://eudml.org/doc/285335>.
@article{T2006, abstract = {The class of all open linear relations is characterised in terms of the restrictions 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.}, author = {T. Álvarez}, journal = {Studia Mathematica}, keywords = {multivalued linear operator; linear relation; linear normed space; open linear relation; semi-Fredholm property; perturbation}, language = {eng}, number = {3}, pages = {205-212}, title = {Characterisations of open multivalued linear operators}, url = {http://eudml.org/doc/285335}, volume = {175}, year = {2006}, }
TY - JOUR AU - T. Álvarez TI - Characterisations of open multivalued linear operators JO - Studia Mathematica PY - 2006 VL - 175 IS - 3 SP - 205 EP - 212 AB - The class of all open linear relations is characterised in terms of the restrictions 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. LA - eng KW - multivalued linear operator; linear relation; linear normed space; open linear relation; semi-Fredholm property; perturbation UR - http://eudml.org/doc/285335 ER -