1. Hille, E., Phillips, R.S.: Functional analysis and semi-groups. Amer. Soc. Math. Colloq. Publ.31 (1957). See also the following book: Joshi, M.C., Bose, R.K.: Some topics in nonlinear functional analysis. New York: Wiley 1985; Rudin, W.: Functional Analysis, New York: McGraw Hill, 1973. In this book, the first-order derivative off(A) is denoted by(Df) A and it is given in a power series of the commutatorC A=RA−LA with the coefficientsf (n)(A)/n!, whereR A andL A denote right and left multiplications ofA, respectively; Deimling, K.: Nonlinear functional analysis. Berlin-Heidelberg-New York: Springer, 1985
2. Nachbin, L.: Topology on Spaces of Holomorphic Mappings. Berlin-Heidelberg-New York: Springer-Verlag, 1969
3. Suzuki, M.: J. Math. Phys.26, 601 (1985)
4. Sakai, S.: Operator Algebra in Dynamical Systems. Cambridge: Cambridge Univ. Press, 1991. See also Karasev, M.V. and Maslov, V.P.: Nonlinear Poisson Brackets—Geometry and Quantization. Trans. Math. Monographs. Vol.119, Providence, RI: Am. Math. Soc., 1993. After the present paper was submitted, Dr. R.I. McLachlan pointed out this reference to the author. Quite similar problems are discussed using different formulations
5. Suzuki, M.: J. Stat. Phys.43, 883 (1986)