Sentence examples for total paranorm space from inspiring English sources

Theorem 2.4. is a paranormed (need not total paranorm) space with (2.3).

A paranorm p for which p ( x ) = 0 implies x = 0 is called a total paranorm and the pair ( X, p ) is called a total paranormed space.

A paranorm w for which w(x) = 0 implies x = 0 is called a total paranorm, and the pair (X,w) is called a total paranormed space.

A paranorm g for which g(x) = 0 implies x = θ is called a total paranorm on X, and the pair (X, g) is called a total paranormed space.

It is paranormed by for all where We recall that a paranormed space is total if implies Every total paranormed space becomes a linear metric space with the metric given by It is clear that is a total paranormed space.

It is well known that the metric of any linear metric space is given by some total paranorm (see[24], Theorem 10.4.2, p.183).

It is well known that the metric of any linear metric space is given by some total paranorm (see [30], Theorem 10.4.2, p.183).

A Fréchet space is a total and complete paranormed space.

which is complete paranormed space paranormed by g ( x ) = ( ∑ k | x k | p k ) 1 M.

For any fixed, is paranormed space with respect to the paranorm defined by (2.8).

Lemma 2.1 Let ( X, { P n be a matrix paranormed space.