Encyclopedia > B-star-algebra

  Article Content

B-star-algebra

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:
  • (x + y)* = x* + y* for all x, y in A
(the involution of the sum of x and y is equal to the sum of the involution of x with the involution of y)
  • x)* = λ* x* for every λ in C and every x in A; here, λ* stands for the complex conjugation of λ.

  • (xy)* = y* x* for all x, y in A
(the involution of the product of x and y is equal to the product of the involution of x with the involution of y)
  • (x*)* = x for all x in A
(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:

  • ||x x*|| = ||x||2 for all x in A.
(the norm of the product of x and the involution of x is equal to the norm of x squared )

See also: algebra.



All Wikipedia text is available under the terms of the GNU Free Documentation License

 
  Search Encyclopedia

Search over one million articles, find something about almost anything!
 
 
  
  Featured Article
East Hampton North, New York

... of age or older. The median age is 41 years. For every 100 females there are 92.6 males. For every 100 females age 18 and over, there are 90.2 males. The median income ...

 
 
 
This page was created in 34.8 ms