Measures of weak noncompactness in Banach spaces

Weak Interpolation in Banach Spaces

Application of measures of noncompactness to infinite system of linear equations in sequence spaces

G. Darbo [Rend. Sem. Math. Univ. Padova, 24 (1955) 84--92] used the measure of noncompactness to investigate operators whose properties can be characterized as being intermediate between those of contraction and compact operators. In this paper, we apply the Darbo's fixed point theorem for solving infinite system of linear equations in some sequence spaces.  

Weak Thresholding Greedy Algorithms in Banach Spaces

We consider weak thresholding greedy algorithms with respect to Markushevich bases in general Banach spaces. We find sufficient conditions for the equivalence of boundedness and convergence of the approximants. We also show that if there is a weak thresholding algorithm for the system which gives the best n-term approximation up to a multiplicative constant, then the system is already “greedy”....

Inequivalent measures of noncompactness

Two homogeneous measures of noncompactness β and γ on an infinite dimensional Banach space X are called “equivalent” if there exist positive constants b and c such that bβ(S) ≤ γ (S) ≤ cβ(S) for all bounded sets S ⊂ X . If such constants do not exist, the measures of noncompactness are “inequivalent.”Weask a foundational questionwhich apparently has not previously been considered: For what infi...

Deviation Measures on Banach Spaces and Applications

In this article we generalize the notion of the deviation measure, which were initially defined on spaces of squarely integrable random variables, as an extension of the notion of standard deviation. We extend them both under a frame which requires some elements from the theory of partially ordered linear spaces and also under a frame which refers to some closed subspace, whose elements are sup...