IJPAM: Volume 21, No. 4 (2005)
THE OPERATIONAL CALCULUS
52900 Ramat-Gan, ISRAEL
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 .
Received: May 9, 2005
AMS Subject Classification: 47A60, 47A63
Key Words and Phrases: operational calculus, Banach space, Hilbert space, Cauchy-type estimates
Source: International Journal of Pure and Applied Mathematics