Multivariable Bergman Shifts and Wold Decompositions View Full Text


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Article Info

DATE

2018-10

AUTHORS

Jörg Eschmeier, Sebastian Langendörfer

ABSTRACT

Let Hm(B) be the analytic functional Hilbert space on the unit ball B⊂Cn with reproducing kernel Km(z,w)=(1-⟨z,w⟩)-m. Using algebraic operator identities we characterize those commuting row contractions T∈L(H)n on a Hilbert space H that decompose into the direct sum of a spherical coisometry and copies of the multiplication tuple Mz∈L(Hm(B))n. For m=1, this leads to a Wold decomposition for partially isometric commuting row contractions that are regular at z=0. For m=1=n, one obtains the classical Wold decomposition of isometries. To prove the above results we extend a corresponding one-variable Wold-type decomposition theorem of Giselsson and Olofsson (Complex Anal Oper Theory 6:829–842, 2012) to the case of the unit ball. More... »

PAGES

56

References to SciGraph publications

  • 2012-08. On Some Bergman Shift Operators in COMPLEX ANALYSIS AND OPERATOR THEORY
  • 2006-10. m-Isometric Commuting Tuples of Operators on a Hilbert Space in INTEGRAL EQUATIONS AND OPERATOR THEORY
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    http://scigraph.springernature.com/pub.10.1007/s00020-018-2481-3

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    http://dx.doi.org/10.1007/s00020-018-2481-3

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