| Abstract: | 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.__________Translated from Funktsional nyi Analiz i Ego Prilozheniya, Vol. 39, No. 1, pp. 69–81, 2005Original Russian Text Copyright © by P. A. TerekhinSupported by the RFBR under grant No. 03-01-00390, the program  Leading Scientific Schools of the Russian Federation under grant No. NSh-1295.2003.1, and the INTAS under grant No. 99-00089.Translated by V. E. Nazaikinskii |
