7 research outputs found
Some Paranormed Difference Sequence Spaces of Order Derived by Generalized Means and Compact Operators
We have introduced a new sequence space
combining by using generalized means and difference operator of order . We
have shown that the space is complete under some
suitable paranorm and it has Schauder basis. Furthermore, the -,
-, - duals of this space is computed and also obtained necessary
and sufficient conditions for some matrix transformations from to . Finally, we obtained some identities or
estimates for the operator norms and the Hausdorff measure of noncompactness of
some matrix operators on the BK space by
applying the Hausdorff measure of noncompactness.Comment: Please withdraw this paper as there are some logical gap in some
results. 20 pages. arXiv admin note: substantial text overlap with
arXiv:1307.5883, arXiv:1307.5817, arXiv:1307.588
Applications of uniform boundedness principle to matrix transformations
Using the uniform boundedness principle of Maddox, we characterize matrix transformations from the space to the spaces and for the case , which correspond to bounded linear operators. Here is the domain of an arbitrary triangle matrix in the space , and the spaces and are introduced by W.L.C. Sargent. In special cases, we get some well known results of W.L.C. Sargent, M. Stieglitz and H. Tietz, E. Malkowsky and E. SavaÅŸ. Also we give other applications including some important new classes