No abstract

In this paper, the mixed norm sequence spaces ?p,q for 1 ? p,q ? ? are the subject of our research; we establish conditions for an operator T? to be compact, where T? is given by a diagonal matrix. This will be achieved by applying the Hausdorff measure of noncompactness and the theory of BK spaces. This problem was treated and solved in [5, 6], but in a different way, without the application of the theory of infinite matrices and BK spaces. Here, we will present a new approach to the problem. Some of our results are known and others are new. [Projekat Ministarstva nauke Republike Srbije, br. 174007 i br. 174025]

We establish some identities or inequalities for the Hausdorff measure of noncompactness for operators L ∈ B(X, Y ) when X = p (1 ≤ p < ∞) and Y = c; X = p (1 < p < ∞) and Y = ∞ ; X = bv 0 and Y = c; X = c 0 (∆), c(∆), ∞ (∆) and Y = ∞ . These identities and estimates are used to establish necessary and sufficient conditions for the operators to be compact. Furthermore, we apply a result by Sargent to establish necessary and sufficient conditions for operators in B(bv 0 , ∞ ) and B( 1 , Y ) to be compact, where Y = w ∞ , v ∞ , [c] ∞ .

Tower", metoda sila, metoda deformacija, armirani beton, prednaprezanje, ram, opterećenje, beton.

Sequence space of convergent series can also be seen as a matrix domain of triangle. By using the theory of matrix domains of triangle, as well as the fact that cs is an AK space we can give the representation of some general bounded linear operators related to the cs sequence space. We will also give the conditions for compactness by using the Hausdorff measure of noncompactness.