Quasinorm

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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 K > 1.

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

[edit] Related concepts

A vector space with an associated quasinorm is called a quasinormed vector space.

A complete quasinormed vector space is a quasi-Banach space.

[edit] See also

• Seminorm

[edit] References

• Aull, Charles E.; Robert Lowen (2001). Handbook of the History of General Topology. Springer. ISBN 079236970X. 
• Conway, John B. (1990). A Course in Functional Analysis. Springer. ISBN 0387972455. 
• Nikolʹskiĭ, Nikolaĭ Kapitonovich (1992). Functional Analysis I: Linear Functional Analysis, Encyclopaedia of Mathematical Sciences 19. Springer. ISBN 3540505849. 
• Swartz, Charles (1992). An Introduction to Functional Analysis. CRC Press. ISBN 0824786432.