Geodesic
Multishifts in Hilbert Spaces
Funkcionalʹnyj analiz i ego priloženiâ, Tome 39 (2005) no. 1, pp. 69-81.

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We introduce and study a multishift structure in a Hilbert space. This structure is a noncommutative analog of the (simple one-sided) shift operator, well known in function theory and functional analysis. Subspaces invariant under the multishift are described. A theorem on the factorization into an inner and an outer factor is established for operators commuting with the multishift.
Keywords: Hilbert space, shift operator, multishift, invariant subspace, wandering subspace, factorization theorem. 
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P. A. Terekhin. Multishifts in Hilbert Spaces. Funkcionalʹnyj analiz i ego priloženiâ, Tome 39 (2005) no. 1, pp. 69-81. http://geodesic.mathdoc.fr/item/FAA_2005_39_1_a5/

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