Abstract
We show the existence of a doubly power-bounded
T
on
L
p
,
1
<
p
<
∞
,
p
≠
2
, such that
T
is spectral of scalar type (hence polynomially bounded),
T
is not similar to a Lamperti operator (hence is not similar to an isometry), none of the powers of
T
is similar to a Lamperti operator, none of the powers is similar to a positive operator, and for some f
∈
L
p the averages
1
n
∑
k
=
1
n
T
kf
(or the averages along the primes or the squares) fail to be a.e. convergent.
Page:
1327-1327
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