Part of the Classics in Mathematics book series (CLASSICS, volume 60)
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Let A be a linear associative algebra over the complex numbers. The algebra A is called a normed algebra if there is associated to each element x a real number ∥x∥, called the norm of x, with the properties:
∥x∥ ≥ 0 and ∥x∥ = 0 if and only if x = 0;
∥x + y∥ ≤ ∥x∥ + ∥y∥;
∥λx∥ = |λ| ∥x∥, λ a complex number;
∥xy∥ ≤ ∥x∥ ∥y∥.
KeywordsBanach Space Positive Element Polar Decomposition Partial Isometry Strong Operator Topology
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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© Springer-Verlag Berlin Heidelberg 1998