SHARP GENERALIZED CARLEMAN INEQUALITIES WITH MINIMAL INFORMATION ABOUT THE SPECTRUM

Let H and T:H --> H denote a separable Hilbert space and an operator i n a Schatten-von Neumann ideal S(p)(H), respectively. Consider the res olvent operator (lambdaI - T)-1, where I is the identity operator and lambda belongs to the resolvent set of T. Some sharp bounds for the un iform operator norm of (lambdaI - T)-1 are derived in some situations of particular interest for certain applications, namely when only part ial or minimal information about the spectrum is available. The result s obtained may also be regarded as generalizations of Carleman's inequ ality for quasinilpotent operators.