Journal of Operator Theory

Volume 62, Issue 1, Summer 2009 pp. 111-123.

Factorisation spatiale

Authors: Gilles Cassier (1) Jean Esterle (2)
Author institution: (1) Universite de Lyon, Lyon, F-69003, France and Universite Lyon 1, Institut Camille Jordan, Villeurbanne cedex, F-69622, France, and CNRS, UMR5208
(2) Universite de Bordeaux, IMB, UMR 5251, 351 Cours de la Liberation, 33405 Talence Cedex, France

Summary: We are firstly interested in finding the best possible compressions for a polynomially bounded operator $T$ that belongs to the class $\mathbb{A}_{1,1}$ introduced by H. Bercovici, C. Foiaș and C. Pearcy in Dual Algebras with Applications to Invariant Subspaces and Dilation Theory, CBMS Regional Conf. Ser. in Math., vol. 56, Amer. Math. Ser., Providence, RI 1985. Then, we use these compressions in order to obtain spatial factorizations, with a single vector, for large classes of lower semicontinuous positive functions $f$, in the sense that there exists a vector $x$ in the Hilbert space $H$ such that $\widehat{f}(n)=\langle T^{-n}x| x\rangle $, for all negative integer numbers $n$.

Keywords: Compressions, dilations, polynomially bounded operators, factorization

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