Circles in the spectrum and the geometry of orbits: a numerical ranges approach

0483702 - MÚ 2018 RIV US eng J - Journal Article
Müller, Vladimír - Tomilov, Y.
Circles in the spectrum and the geometry of orbits: a numerical ranges approach.
Journal of Functional Analysis. Roč. 274, č. 2 (2018), s. 433-460. ISSN 0022-1236. E-ISSN 1096-0783
R&D Projects: GA ČR(CZ) GA14-07880S
EU Projects: European Commission(XE) 318910 - AOS
Institutional support: RVO:67985840
Keywords : spectrum * orbits of linear operators * numerical range * convergence of operator iterates
OECD category: Pure mathematics
Impact factor: 1.637, year: 2018
http://www.sciencedirect.com/science/article/pii/S0022123617304111?via%3Dihub

We prove that a bounded linear Hilbert space operator has the unit circle in its essential approximate point spectrum if and only if it admits an orbit satisfying certain orthogonality and almost -orthogonality relations. This result is obtained via the study of numerical ranges of operator tuples where several new results are also obtained. As consequences of our numerical ranges approach, we derive in particular wide generalizations of Arveson's theorem as well. as show that the weak convergence of operator powers implies the uniform convergence of their compressions on an infinite-dimensional subspace.
Permanent Link: http://hdl.handle.net/11104/0278907