Decomposition of fréchet Q lmc*- algebra - Azram, Mohammad (2015)
This paper is devoted to discuss the new approach to define inner product space Aμ on a unital commutative semi-simple separable Fréchet Q lmc*- algebra via the Gelfand transformation by mean of probability measure μ on the maximal ideal space Δ of A. We will establish that every maximal ideal M of A with M┴ ≠ {0} is Aμ -closed and consequently the decomposition A = M ⊕ M ⊥.