FUNCTIONAL-CALCULUS AND FRACTIONAL POWER OF MULTIVALUED NONNEGATIVE LINEAR-OPERATORS

We extend some results of functional calculus to multivalued nonnegative linear operators A in Banach spaces. In particular, we study the fractional power A-alpha for 0 < alpha < 1, and prove that A-alpha + beta = A-alpha A-beta, (A-1)-alpha = (A-alpha)-1 for alpha, beta > 0 with alpha + beta > 0 with alpha + beta less-than-or-equal-to 1, as well as [GRAPHICS]