Joint numerical ranges: Recent advances and applications minicourse by V. Müller and Yu. Tomilov

0532938 - MÚ 2021 RIV PL eng J - Journal Article
Müller, Vladimír - Tomilov, Y.
Joint numerical ranges: Recent advances and applications minicourse by V. Müller and Yu. Tomilov.
Concrete Operators. Roč. 7, č. 1 (2020), s. 133-154. E-ISSN 2299-3282
R&D Projects: GA ČR(CZ) GX20-31529X
Institutional support: RVO:67985840
Keywords : operator tuples * numerical range * essential numerical range
OECD category: Pure mathematics
Method of publishing: Open access
https://doi.org/10.1515/conop-2020-0102

We present a survey of some recent results concerning joint numerical ranges of n-tuples of Hilbert space operators, accompanied with several new observations and remarks. Thereafter, numerical ranges techniques will be applied to various problems of operator theory. In particular, we discuss problems concerning orbits of operators, diagonals of operators and their tuples, and pinching problems. Lastly, motivated by known results on the numerical radius of a single operator, we examine whether, given bounded linear operators T1, . . . , Tn on a Hilbert space H, there exists a unit vector x 2 H such that jhTjx, xij is “large” for all j = 1, . . . , n.
Permanent Link: http://hdl.handle.net/11104/0311317