Functional Equation over Hilbert Spaces.

摘要

In this note we answer a problem proposed by Watatani and show that if alpha , beta are commuting unitary operators on a Hilbert space H satisfying the equation alpha + alpha /sup -1/= beta + beta /sup -1/, then H can be decomposed by a projection p on H such that alpha = beta on pH and alpha = beta /sup -1/ on (1-p)H. We also prove a similar decomposition result for one-parameter groups of unitary operators on H. (author). 12 refs. (Atomindex citation 19:059911)