The joint essential numerical range, compact perturbations, and the Olsen problem

0342843 - MÚ 2011 RIV PL eng J - Journal Article
Müller, Vladimír
The joint essential numerical range, compact perturbations, and the Olsen problem.
Studia mathematica. Roč. 197, č. 3 (2010), s. 275-290. ISSN 0039-3223. E-ISSN 1730-6337
R&D Projects: GA ČR GA201/09/0473; GA AV ČR IAA100190903
Institutional research plan: CEZ:AV0Z10190503
Keywords : joint essential numerical range * joint numerical range * compact perturbation * Olsen's problem
Subject RIV: BA - General Mathematics
Impact factor: 0.567, year: 2010
http://journals.impan.pl/cgi-bin/doi?sm197-3-5

Let T be an n-tuple of bounded linear operators on a complex Hilbert space H. Then there exists an n-tuple K of compact operators such that the essential numerical range of T equals to the closure of the numerical range of T+K. This generalices the corresponding resoult for n=1. The result is also applied to the Olsen problem.
Permanent Link: http://hdl.handle.net/11104/0185464