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Matematicheskie Zametki, 2007, Volume 82, Issue 6, Pages 894–904
DOI: https://doi.org/10.4213/mzm4189
(Mi mzm4189)
 

Wold Decomposition in Banach Spaces

A. V. Romanov

Moscow State Institute of Electronics and Mathematics (Technical University)
References:
Abstract: We propose a natural analog of the Wold decomposition in the case of a linear noninvertible isometry $V$ in a Banach space $X$. We obtain a criterion for the existence of such a decomposition. In a reflective space, this criterion is reduced to the existence of the linear projection $P\colon X\to V\!X$ with unit norm. Separately, we discuss the problem of the Wold decomposition for the isometry $V_\varphi$ induced by an epimorphism $\varphi$ of a compact set $H$ in the space of continuous functions $C(H)$. We present a detailed study of the mapping $z\to z^m$ of the circle $|z|=1$ with an integer $m\ge2$.
Keywords: Wold decomposition, linear noninvertible isometry, Banach space, reflexive space, unitary operator, completely nonunitary isometry, one-sided shift.
Received: 19.01.2007
Revised: 17.04.2007
English version:
Mathematical Notes, 2007, Volume 82, Issue 6, Pages 806–815
DOI: https://doi.org/10.1134/S0001434607110259
Bibliographic databases:
UDC: 517.983.23
Language: Russian
Citation: A. V. Romanov, “Wold Decomposition in Banach Spaces”, Mat. Zametki, 82:6 (2007), 894–904; Math. Notes, 82:6 (2007), 806–815
Citation in format AMSBIB
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