This is the abstract of the paper "The $H^\infty$-calculus and sums of closed operators" by Nigel J. Kalton and Lutz Weis. For the whole paper send the command get evolve-l 01-00026 to: "listserv@uni-karlsruhe.de". Instead you may get the paper at "http://ma1serv.mathematik.uni-karlsruhe.de/evolve-l/index.html" too. Abstract: We develop a very general operator-valued functional calculus for operators with an $H^\infty$-calculus. We then apply this to the joint functional calculus of two sectorial operators when one has an $H^\infty$-calculus. Using this we prove theorem of Dore-Venni type on sums of sectorial operators and apply our results to the problem of $L_p$-maximal regularity. Our main assumption is the $R$-boundedness of certain sets of operators, and therefore methods form the geometry of Banach spaces are essential here. In the final section we exploit the special Banach structure of $L_1$-spaces and $C(K)$-spaces, to obtain some more detailed results in this setting. ------------------ http://www.uni-karlsruhe.de/~listserv/ ------------------