This article is cited in 14 papers

Multishifts in Hilbert Spaces

P. A. Terekhin

Saratov State University named after N. G. Chernyshevsky

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.

Keywords: Hilbert space, shift operator, multishift, invariant subspace, wandering subspace, factorization theorem.

UDC: 517.5

Received: 19.03.2003

DOI: 10.4213/faa32

 English version: Functional Analysis and Its Applications, 2005, 39:1, 57–67

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