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

0532938 - MÚ 2021 RIV PL eng J - Článek v odborném periodiku
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
Grant CEP: GA ČR(CZ) GX20-31529X
Institucionální podpora: RVO:67985840
Klíčová slova: operator tuples * numerical range * essential numerical range
Obor OECD: Pure mathematics
Způsob publikování: 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.
Trvalý link: http://hdl.handle.net/11104/0311317