# Michael Hartz: von Neumann's inequality on the disc and on the polydisc

V četrtek, 3. 10. 2024, bo v okviru Matematičnih kolokvijev predavanje z naslovom

**von Neumann's inequality on the disc and on the polydisc**

Michael Hartz, Universit\" at des Saarlandes, Nemčija

Povzetek predavanja:

von Neumann's inequality provides a fundamental link between analytic functions on the unit disc and contraction matrices, or more generally contraction operators on Hilbert space. It asserts that if $T$ is a contraction and $p$ is a polynomial, then$$ |p(T)| \le \sup { |p(z)| : |z| \le 1 }.$$

The multivariable setting turns out to be significantly more complicated. Whereas And\^o extended this inequality to pairs of commuting contractions, the corresponding statement for triples of commuting contractions is false. The first counterexamples were found in the early seventies, but this phenomenon is still not well understood and many questions remain open.

I will talk about the original inequality and some of the challenges in several variables. In particular, I will talk about the question of whether von Neumann's inequality for triples of commuting contractions holds up to a constant.

Kolokvij bo v predavalnici 2.02 na Jadranski 21 ob 15:15. Po predavanju sledi druženje ob prigrizkih.

Vljudno vabljeni. Primož Moravec