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

for some ${\displaystyle K>0.}$

This is not to be confused with a seminorm or pseudonorm, where the norm axioms are satisfied except for positive definiteness.

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 ${\displaystyle (A,\|\cdot \|)}$ is called a quasinormed algebra if the vector space A is an algebra and there is a constant K > 0 such that

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