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Admissible fundamental operators(star)

Bhattacharyya, Tirthankar and Lata, Sneh and Sau, Haripada (2015) Admissible fundamental operators(star). In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 425 (2). pp. 983-1003.

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


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 Gamma-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 Gamma-contractions are then applied to tetrablock contractions to figure out when two pairs (F1, F2) 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. (C) 2015 Elsevier Inc. All rights reserved.

Item Type: Journal Article
Additional Information: Copy right for this article belongs to the ACADEMIC PRESS INC ELSEVIER SCIENCE, 525 B ST, STE 1900, SAN DIEGO, CA 92101-4495 USA
Keywords: Spectral set; Symmetrized bidisc; Gamma-contraction; Fundamental operator; Admissible pair; Tetrablock
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 01 Apr 2015 12:08
Last Modified: 01 Apr 2015 12:08
URI: http://eprints.iisc.ac.in/id/eprint/51124

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