[Home]B-star-algebra

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B*-algebras are mathematical structures studied in functional analysis. A B*-algebra A is a Banach algebra over the field of complex numbers, together with a map * : A -> A called involution which has the follow properties:
(the involution of the sum of x and y is equal to the sum of the involution of x with the involution of y)

(the involution of the product of x and y is equal to the product of the involution of x with the involution of y)
(the involution of the involution of x is equal to x)

If the following property is also true, the algebra is actually a '''C*-algebra''':

(the norm of the product of x and the involution of x is equal to the norm of x squared )

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Last edited November 24, 2001 3:58 am by BenBaker (diff)
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