On Some Functional Equations Associated With Semigroups of Operators

Abstract

1. Introduction.-Let X be a Banach space, and let E(X) denote the Banach algebra of endomorphisms of X. A one-parameter family of operator-valued functions { T(t), t E R+I, where T(t): R+ E 8(X), is said to be a semigroup of operators in X if T(s + t) = T(s)T(t), s, t E R+

Systems of trigonometric functional equations in Banach algebras

“…B. Buche in [2] and A. B. Buche, A. T. Bharucha-Reid in [3] investigated a system of addition formulas for functions defined on (0, +∞) and taking values in the Banach algebra of endomorphisms of a Banach space.…”