Sentence examples for be a normed sequence from inspiring English sources

Let ((X,VertcdotVert_{X})) be a normed sequence space and (d=(d_{k})) be a sequence in X.

Let X be a normed sequence space, T a triangle, and ({chi}_{T}) and χ denote the Hausdorff measure of noncompactness on (M_{{X}_{T}}) and (M_{X}).

If ( ∥ ⋅ ∥, X ) is a normed sequence space, then we write ∥ a ∥ X ∗ sup x ∈ S X ∑ k = n ∞ | a k x k | (3.1).

More generally if μ is a normed sequence space, we can write D μ ( A ) for x ∈ ω, for which the sum in (1.1) converges in the norm of μ.

A linear space is called a normed sequence space if there is a mapping such that (i) if and only if ;   (ii), for all ;   (iii), for all ;   (iv) if have the property that, for all and, then and.  . if and only if ;, for all ;, for all ; if have the property that, for all and, then and.

Let be a normed space with norm.

Let X be a normed space and (x=(x_{k})) be a sequence in X.

Let X be a normed space and (g=(g_{i})) be a sequence in (X^).

Let be a normed space.

Let (mathcal {A}) be a normed algebra.

Let ( X, ∥ ⋅ ∥ ) be a normed space.