Admissible fundamental operators☆

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:425

Article

Bhattacharyya, Tirthankar¹  Lata, Sneh²  Sau, Haripada¹ 

[1] Indian Inst Sci, Dept Math, Bangalore 560012, Karnataka, India

[2] Shiv Nadar Univ, Sch Nat Sci, Dept Math, Gautam Budh Nagar 208207, Uttar Pradesh, India

关键词: Spectral set;    Symmetrized bidisc;    Gamma-contraction;    Fundamental operator;    Admissible pair;    Tetrablock;   

DOI  :  10.1016/j.jmaa.2015.01.006

来源: Elsevier

【 摘 要 】

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.

【 授权许可】

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