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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.
MSC:
46A45Sequence spaces
40H05Functional analytic methods in summability
46B45Banach sequence spaces
47B37Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)