A Characterization of Extremal Sets in Hilbert Spaces
We give a characterization of extremal sets in Hilbert spaces that generalizes a classical theorem of H. W. E. Jung. We investigate also the behaviour of points near to the circumsphere of such a set with respect to the Kuratowski and Hausdorff measures of non-compactness.
The radius of a compact set in a Hilbert space
AbstractIn this note we improve the formular(A)⩽
$$\frac{1}{{\sqrt 2 }}$$
δ(A) proved by Routledge for Hilbert spaces. We show that if A is a relatively compact set, thenr(A)<
$$\frac{1}{{\sqrt 2 }}$$
δ(A)
Representations and computations of {2, 3~} and {2, 4~}-inverses in indefinite inner product spaces
We investigate full-rank representations of { 2 , 3 ~ } and { 2 , 4 ~ } -inverses with prescribed rank as well as with prescribed range and null space in an indefinite inner product space. In certain particular cases we obtain new results or generalizations related with { 2 , 3 } and { 2 , 4 } -inverses in a Hilbert (unitary) space. Direct and iterative methods for computing { 2 , 3 ~ } and { 2 , 4 ~ } -inverses in an indefinite inner product space are developed. Numerical examples with different metric matrices are presented.