# Wold-type extension for N-tuples of commuting contractions

Studia Mathematica (1999)

- Volume: 137, Issue: 1, page 81-91
- ISSN: 0039-3223

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topKosiek, Marek, and Octavio, Alfredo. "Wold-type extension for N-tuples of commuting contractions." Studia Mathematica 137.1 (1999): 81-91. <http://eudml.org/doc/216676>.

@article{Kosiek1999,

abstract = {Let (T1,…,TN) 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 (V1,…,VN) of contractions on a superspace K of ℋ such that each $V_j$ extends $T_j$, j=1,…,N, and the N-tuple (V1,…,VN) 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])},

author = {Kosiek, Marek, Octavio, Alfredo},

journal = {Studia Mathematica},

keywords = {contractions; dilations; extensions; alternative dilation theory; Wold-type decomposition},

language = {eng},

number = {1},

pages = {81-91},

title = {Wold-type extension for N-tuples of commuting contractions},

url = {http://eudml.org/doc/216676},

volume = {137},

year = {1999},

}

TY - JOUR

AU - Kosiek, Marek

AU - Octavio, Alfredo

TI - Wold-type extension for N-tuples of commuting contractions

JO - Studia Mathematica

PY - 1999

VL - 137

IS - 1

SP - 81

EP - 91

AB - Let (T1,…,TN) 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 (V1,…,VN) of contractions on a superspace K of ℋ such that each $V_j$ extends $T_j$, j=1,…,N, and the N-tuple (V1,…,VN) 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])

LA - eng

KW - contractions; dilations; extensions; alternative dilation theory; Wold-type decomposition

UR - http://eudml.org/doc/216676

ER -

## References

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- [2] H. Bercovici, Commuting power-bounded operators, Acta Sci. Math. (Szeged) 57 (1993), 55-64. Zbl0819.47017
- [3] H. Bercovici, C. Foiaş, and C. Pearcy, Dual Algebras with Applications to Invariant Subspaces and Dilation Theory, CBMS Regional Conf. Ser. in Math. 56, Amer. Math. Soc., Providence, RI, 1985. Zbl0569.47007
- [4] L. Kérchy, Unitary asymptotes of Hilbert space operators, in: Functional Analysis and Operator Theory, Banach Center Publ. 30, Inst. Math., Polish Acad. Sci., Warszawa, 1994, 191-201. Zbl0807.47005
- [5] M. Kosiek and A. Octavio, On common invariant subspaces for N-tuples of commuting contractions with rich spectrum, to appear. Zbl1061.47007
- [6] M. Kosiek, A. Octavio, and M. Ptak, On the reflexivity of pairs of contractions, Proc. Amer. Math. Soc. 123 (1995), 1229-1236. Zbl0836.47006
- [7] M. Kosiek and M. Ptak, Reflexivity of n-tuples of contractions with rich joint left essential spectrum, Integral Equations Operator Theory 13 (1990), 395-420. Zbl0743.47032
- [8] A. Octavio, Coisometric extension and functional calculus for pairs of contractions, J. Operator Theory 31 (1994), 67-82. Zbl0872.47009
- [9] M. Słociński, On the Wold type decomposition of a pair of commuting isometries, Ann. Polon. Math. 37 (1980), 255-262. Zbl0485.47018
- [10] B. Sz.-Nagy and C. Foiaş, Harmonic Analysis of Operators on Hilbert Space, North-Holland, Amsterdam, 1970. Zbl0201.45003

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