A general approach to the notion of Silov boundary

1989 ◽  
Vol 202 (3) ◽  
pp. 391-395 ◽  
Author(s):  
Przemys?aw Kajetanowicz
Keyword(s):  
Šilov Boundary ◽  
Silov Boundary

Boundaries For Real Banach Algebras

1976 ◽  
Vol 28 (1) ◽  
pp. 42-49 ◽  
Author(s):  
B. V. Limaye
Keyword(s):  
Banach Algebra ◽  
Maximal Ideal ◽  
Banach Algebras ◽  
Maximal Ideal Space ◽  
Close Connection ◽  
Ideal Space ◽  
The Real ◽  
Šilov Boundary ◽  
The Absolute ◽  
Silov Boundary

Let A be a commutative real Banach algebra with unit, and MA its maximal ideal space. The existence of the Silov boundary SA for A was established in [5] by resorting to the complexification of A. We give here an intrinsic proof of this result which exhibits the close connection between the absolute values and the real parts of ‘functions’ in A (Theorem 1.3).

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