Bhattacharyya, Tirthankar ; Lata, Sneh ; Sau, Haripada
(2015)
*Admissible fundamental operators*
Journal of Mathematical Analysis and Applications, 425
(2).
pp. 983-1003.
ISSN 0022-247X

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Official URL: http://www.sciencedirect.com/science/article/pii/S...

Related URL: http://dx.doi.org/10.1016/j.jmaa.2015.01.006

## Abstract

Let F and G be two bounded operators on two Hilbert spaces. Let their numerical radii be no greater than one. This note investigates when there is a Γ-contraction (S,P) such that F is the fundamental operator of (S,P) and G is the fundamental operator of (S*,P*). Theorem 1 puts a necessary condition on F and G for them to be the fundamental operators of (S,P) and (S*,P*) respectively. Theorem 2 shows that this necessary condition is also sufficient provided we restrict our attention to a certain special case. The general case is investigated in Theorem 3. Some of the results obtained for Γ-contractions are then applied to tetrablock contractions to figure out when two pairs (F_{1},F_{2}) and (G_{1},G_{2}) acting on two Hilbert spaces can be fundamental operators of a tetrablock contraction (A,B,P) and its adjoint (A*,B*,P*) respectively. This is the content of Theorem 3.

Item Type: | Article |
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Source: | Copyright of this article belongs to Elsevier Science. |

Keywords: | Spectral Set; Symmetrized Bidisc; Γ-Contraction; Fundamental Operator; Admissible Pair; Tetrablock |

ID Code: | 99709 |

Deposited On: | 27 Nov 2016 12:52 |

Last Modified: | 27 Nov 2016 12:52 |

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