75 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
Wold decomposition for isometries with equal range
This paper presents the structure for -tuple of isometries acting on a
Hilbert space. More precisely, we prove that -tuple () of
isometries on a Hilbert space with
and
for , where admits a unique Wold
decomposition. Our results unify all prior findings on the decomposition of
-tuples of isometries in the existing literature.Comment: 23 pages. Preliminary versio
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