The one-sided ergodic Hilbert transform in Banach spaces

作者：Cohen Guy^*; Cuny Christophe; Lin Michael

来源：Studia Mathematica, 2010, 196(3): 251-263.

DOI：10.4064/sm196-3-3

• ergodic Hilbert transform
• operator power series
• measure preserving transformations
• semigroup of fractional powers

Let T be a power-bounded operator on a (real or complex) Banach space. We study the convergence of the one-sided ergodic Hilbert transform lim(n) Sigma(n)(k=1) T(k)x/k. We prove that weak and strong convergence. are equivalent, and in a reflexive Space also sup(n) parallel to Sigma(n)(k=1) T(k)x/k parallel to < infinity is equivalent to the convergence. We also show that - Sigma(infinity)(k=1) T-k/k (which converges on (I - T)X) is precisely the infinitesimal generator of the semigroup (I - T)(r) <(vertical bar(I-T)X)over bar>.

• 出版日期2010