# 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

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 is called a **quasinormed algebra** if the vector space *A* is an algebra and there is a constant *K* > 0 such that

for all .

A complete quasinormed algebra is called a **quasi-Banach algebra**.

## See also

## References

- Aull, Charles E.; Robert Lowen (2001).
*Handbook of the History of General Topology*. Springer. ISBN 0-7923-6970-X. - Conway, John B. (1990).
*A Course in Functional Analysis*. Springer. ISBN 0-387-97245-5. - Nikolʹskiĭ, Nikolaĭ Kapitonovich (1992).
*Functional Analysis I: Linear Functional Analysis*. Encyclopaedia of Mathematical Sciences.**19**. Springer. ISBN 3-540-50584-9. - Swartz, Charles (1992).
*An Introduction to Functional Analysis*. CRC Press. ISBN 0-8247-8643-2.

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