On the limit of square-Cesàro means of contractions on Hilbert spaces

摘要

By combining tools from functional analysis and algebraic number theory, we investigate the qualitative properties of the square-Cesàro means, where T is a contraction on a Hilbert space. The existence of their limit in the strong operator topology as N → ∞ is known even for general polynomial sequences, but the limit itself has not yet been studied apart from the linear case solved by the von Neumann Ergodic Theorem. The case of the sequence n~2 is the next step beyond this linear case, and we show that even though the limit operator is generally not a projection, it still has a relatively simple and interesting structure.