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Matrix transformations between the sequence space bv p and certain BK spaces. (English) Zbl 1033.46002
Let ω be the set of all complex sequences x=(x k ) k=0 , 1p<, and bv p ={xω: k=0 |x k -x k-1 | p <}. For Xω, its β-dual is defined as X β ={aω: k=0 a k x k convergesforallxX}. The authors determine the β-duals of the sets bv p , characterize some matrix transformations between these sets and apply the Hausdorff measure of noncompactness to give necessary and sufficient conditions for the entries of an infinite matrix to be a compact operator between the space bv p and certain BK-spaces, where a Banach space is said to be BK if its convergence implies coordinatewise convergence.
46A45Sequence spaces
40H05Functional analytic methods in summability
46B45Banach sequence spaces
47B37Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)