CHAPTER 8. COMPLEX NUMBERS Why do we need complex numbers?
... All other elementary identities concerning multiplication are more or less from these three. For example, the well-known identity (a + b)2 = a2 + 2ab + b2 can be derived as follows: (a + b)2 = (a + b)(a + b) = a(a + b) + b(a + b) = aa + ab + ba + bb = a2 + ab + ab + b2 = a2 + 2ab + b2 . Another impo ...
... All other elementary identities concerning multiplication are more or less from these three. For example, the well-known identity (a + b)2 = a2 + 2ab + b2 can be derived as follows: (a + b)2 = (a + b)(a + b) = a(a + b) + b(a + b) = aa + ab + ba + bb = a2 + ab + ab + b2 = a2 + 2ab + b2 . Another impo ...
ON BOUNDED MODULE MAPS BETWEEN HILBERT MODULES OVER LOCALLY C -ALGEBRAS
... A locally C ∗ -algebra is a complete Hausdorff complex topological ∗-algebra A whose topology is determined by its continuous C ∗ -seminorms in the sense that the net {ai }i converges to 0 if and only if the net {p(ai )}i converges to 0 for every continuous C ∗ -seminorm p on A. In fact a locally C ...
... A locally C ∗ -algebra is a complete Hausdorff complex topological ∗-algebra A whose topology is determined by its continuous C ∗ -seminorms in the sense that the net {ai }i converges to 0 if and only if the net {p(ai )}i converges to 0 for every continuous C ∗ -seminorm p on A. In fact a locally C ...
