Admissible fundamental operators

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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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 (F1,F2) and (G1,G2) 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
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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