Geodesic
Wold Decomposition in Banach Spaces
Matematičeskie zametki, Tome 82 (2007) no. 6, pp. 894-904

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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. 
@article{MZM_2007_82_6_a9,
     author = {A. V. Romanov},
     title = {Wold {Decomposition} in {Banach} {Spaces}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {894--904},
     publisher = {mathdoc},
     volume = {82},
     number = {6},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2007_82_6_a9/}
}
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A. V. Romanov. Wold Decomposition in Banach Spaces. Matematičeskie zametki, Tome 82 (2007) no. 6, pp. 894-904. http://geodesic.mathdoc.fr/item/MZM_2007_82_6_a9/