# IJPAM: Volume 21, No. 4 (2005)

CAUCHY ESTIMATES FOR
THE OPERATIONAL CALCULUS

S. Kantorovitz
Bar-Ilan University
52900 Ramat-Gan, ISRAEL
e-mail: kantor@math.biu.ac.il

Abstract.Let be a (linear, not necessarily bounded) operator on a Banach space , whose resolvent contains the open unit disc (or the set ), and whose resolvent operator satisfies the inequality for all (or , respectively). We show that for all and (, respectively). In case is Hilbert space, and is a contraction satisfying in , one has for all and . These resolvent estimates imply Cauchy-type estimates for .