Mean ergodic type theorems
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Date
2019-08-01
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Ankara Üniversitesi Fen Fakültesi
Abstract
Let
T
be a bounded linear operator on a Banach space
X
. Replacing the Ces\`{a}ro matrix by a regular matrix
A
=
(
a
n
j
)
Cohen studied a mean ergodic theorem. In the present paper we extend his result by taking a sequence of infinite matrices
A
=
(
A
(
i
)
)
that contains both convergence and almost convergence. This result also yields an
A
-ergodic decomposition. When
T
is power bounded we give a characterization for
T
to be
A
-ergodic.
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Keywords
Infinite matrices, Almost convergence, Ergodic theorems