Normed algebra

In mathematics, a normed algebra A is an algebra over a field which has a sub-multiplicative norm:

∀ x , y ∈ A ‖ x y ‖ ≤ ‖ x ‖ ‖ y ‖ . {\displaystyle \forall x,y\in A\qquad \|xy\|\leq \|x\|\|y\|.}

Some authors require it to have a multiplicative identity 1A such that ║1A║ = 1.

See also

  • Banach algebra
  • Composition algebra
  • Division algebra
  • Gelfand–Mazur theorem
  • Hurwitz's theorem (composition algebras)

External reading

  • "Normed Algebra". Encyclopaedia of Mathematics. Retrieved 20 May 2018.


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