Wold-type extension for N-tuples of commuting contractions

Marek Kosiek; Alfredo Octavio

ArticleOriginal scientific text

Title

Wold-type extension for N-tuples of commuting contractions

Authors ¹, ²

Affiliations

Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland
IVIC, Departamento de Matemáticas, Apartado 21827 Caracas, 1020A, Venezuela

Abstract

Let (T_1,…,T_N) be an N-tuple of commuting contractions on a separable, complex, infinite-dimensional Hilbert space ℋ. We obtain the existence of a commuting N-tuple (V_1,…,V_N) of contractions on a superspace K of ℋ such that each

V_{j}

extends

T_{j}

, j=1,…,N, and the N-tuple (V_1,…,V_N) has a decomposition similar to the Wold-von Neumann decomposition for coisometries (although the

V_{j}

need not be coisometries). As an application, we obtain a new proof of a result of Słociński (see [9])

Keywords

ENG

contractions, dilations, extensions

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Title

Wold-type extension for N-tuples of commuting contractions

Affiliations

Abstract

Keywords

Bibliography