Multilinear mappings and estimates of multiplicity (Q1091579)

This paper deals with a general duality method for obtaining lower estimates for the multiplicity of an operator on a Banach space. As an application the author obtains a sharpening of a result of B. Sz.-Nagy and C. Foias on the multiplicity of powers of a certain type of completely nonunitary contraction operators on a Hilbert space which bypasses the theory of unitary dilations. Other results include an estimate for the multiplicity of a direct sum of operators, and a simple direct proof that the multiplicity (i.e. the cardinality of a minimal set of vectors for which the algebra of the operator acting on the set generates a dense set) of a normal operator agrees with its spectral multiplicity.