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Quasinorm : ウィキペディア英語版
Quasinorm
In linear algebra, functional analysis and related areas of mathematics, a quasinorm is similar to a norm in that it satisfies the norm axioms, except that the triangle inequality is replaced by
:\|x + y\| \leq K(\|x\| + \|y\|)
for some K > 1.
This is not to be confused with a seminorm or pseudonorm, where the norm axioms are satisfied except for positive definiteness.
== Related concepts ==
A vector space with an associated quasinorm is called a quasinormed vector space.
A complete quasinormed vector space is called a quasi-Banach space.
A quasinormed space (A, \| \cdot \|) is called a quasinormed algebra if the vector space ''A'' is an algebra and there is a constant ''K'' > 0 such that
:\|xy\| \leq K \|x\| \cdot \|y\|
for all x, y \in A.
A complete quasinormed algebra is called a quasi-Banach algebra.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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