Sentence examples similar to continuous with the norm from inspiring English sources

(2) Suppose that (C [-tau_{max},0],mathC [-tau_{max}is the Banach space of continuous functions with the norm biglVert phi_{i} (t) bigrVert =sup_{-tau_{max}leq sleq0} biglVert phi_{i} (t) bigrVert.

Let (E=C[0,1]times C[0,1]) be the Banach space of all continuous functions with the norm biglVert (x_{1},x_{2}) bigrVert = Vert x_{1} Vert + Vert x_{2} Vert,qquad Vert x_{i} Vert =maxbigl{ x_{i}(t): t in[0,1]bigr}.

Sometimes (mathcal{E}) is a subset of a normed linear space (mathcal{X}) of continuous functions endowed with the norm (|cdot|_{mathcal{X}}).

Let (C J,mathbb{R}) = {u Jtomathbb{R}: u(t mbox{ is continuous}}) with the norm (Vert uVert _{C} = sup_{tin J}|u(t)|).

Let denote the Banach space of continuous functions, endowed with the norm (1.1).

Denote as the space of continuous function on with the norm.

Let be the Banach space of all real-valued continuous functions endowed with the norm.

We denote by the space of -valued continuous functions on with the norm (2.1).

Let be a Banach space of all continuous functions from with the norm.

Let denote the Banach space of all continuous functions, equipped with the norm Let for each and for each For we say that is in if is measurable and in which case we define its norm by (13).

The space (C J,mathbb{R})) of all continuous functions endowed with the norm (Vert x Vert =sup_{t in J} vert x t) vert ) is a Banach algebra.