Sentence examples for be a sequence space from inspiring English sources
Let X be a sequence space and denote by Z(X) the subset of X formed by sequences having only a finite number of zero coordinates.
Let Y be a sequence space and (A=({a}_{nk})) be an infinite matrix.
Let (K ={n_{i}in{mathbb{N}}: n_{1}< n_{2}be a sequence space.
Lemma 3.7 Let X be any of the spaces c 0 ( B ) or ℓ ∞ ( B ), let Y be the respective one of the spaces c 0 or ℓ ∞, Z be a sequence space and A = ( a n k ) be an infinite matrix.
Let Z be a sequence space, then Kizmaz [1] introduced the following difference sequence spaces: Z(Delta)=bigl{ (x_{k})in w:(Delta x_{k})in Zbigr} for (Z=ell_{infty},c,c_{0}), where (Delta x_{k}=x_{k}-x_{k+1}) for each (kinmathbb{N}={1,2,3,ldots}), the set of positive integers.
which is a sequence space.
If E is a sequence space, the following are equivalent.
It is obvious that (X r,s,t)) is a sequence space whenever X is a sequence space, and we call it the sequence space of generalized means.
(1) It is obvious that (lambda_{A}) is a sequence space.
It is clear that if X is a sequence space, then (X r,s,t Delta)) is a sequence space too and we call that the difference sequence space derived by using generalized means.
