Bala, Neeru and Ramesh, G.
(2021)
A BishopPhelpsBollobás type property for minimum attaining operators.
Operators and Matrices (2).
pp. 497513.
ISSN 18463886
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Abstract
t. In this article, we study the BishopPhelpsBollob´as type theorem for minimum attaining operators. More explicitly, if we consider a bounded linear operator T on a Hilbert space
H and a unit vector x0 ∈ H such that T x0 is very close to the minimum modulus of T , then
T and x0 are simultaneously approximated by a minimum attaining operator S on H and a
unit vector y ∈ H for which Sy is equal to the minimum modulus of S . Further, we extend
this result to a more general class of densely defined closed operators (need not be bounded) in
Hilbert space. As a consequence, we get the denseness of the set of minimum attaining operators
in the class of densely defined closed operators with respect to the gap metric.
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