Abstract
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:
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I
∥x∥ ≥ 0 and ∥x∥ = 0 if and only if x = 0;
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II
∥x + y∥ ≤ ∥x∥ + ∥y∥;
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III
∥λx∥ = |λ| ∥x∥, λ a complex number;
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IV
∥xy∥ ≤ ∥x∥ ∥y∥.
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© 1998 Springer-Verlag Berlin Heidelberg
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Sakai, S. (1998). General Theory. In: C*-Algebras and W*-Algebras. Classics in Mathematics, vol 60. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-61993-9_1
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DOI: https://doi.org/10.1007/978-3-642-61993-9_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-63633-5
Online ISBN: 978-3-642-61993-9
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