Abstract. Every element of a complex Banach algebra (A, || • ||) is a topological divisor of zero, if at least one of the following holds: (i) A is infinite dimensional and admits an orthogonal basis, (ii) A is a nonunital uniform Banach algebra in which the Silov boundary dA coincides with the Gelfand space A(A) ; and (iii) A is a nonunital hermitian Banach *-algebra with continuous involution. Several algebras of analysis have this property. Examples are discussed to show that (a) neither hermiticity nor dA = A(A) can be omitted, and that (b) in case (ii), dA = &(A) is not a necessary condition.

A predictability index for time series of a financial market vector consisting of chosen market parameters is suggested providing a measure of long range predictability of the market. It is based on fractional Brownian motion that includes Brownian motion as a particular case followed by the time series of financial market parameters. By analyzing respective time series, these indices are computed for parameters like volatility, FII investments in the local market, IIP numbers, CPI numbers, Dow Jones Index, different stock market indices, currency rates, and gold prices.