
theorem Th14:
  for X be ComplexNormSpace holds Ring_of_BoundedLinearOperators(X) is Ring
proof
  let X be ComplexNormSpace;
  for x,y,z being Element of Ring_of_BoundedLinearOperators(X) holds x+y =
  y+x & (x+y)+z = x+(y+z) & x+(0.Ring_of_BoundedLinearOperators(X)) = x & x is
right_complementable & (x*y)*z = x*(y*z) & x*(1.Ring_of_BoundedLinearOperators(
X)) = x & (1.Ring_of_BoundedLinearOperators(X))*x = x & x*(y+z) = x*y + x*z & (
  y+z)*x = y*x + z*x by Th13;
  hence thesis by ALGSTR_0:def 16,GROUP_1:def 3,RLVECT_1:def 2,def 3,def 4
,VECTSP_1:def 6,def 7;
end;
