Department of

Mathematics

Seminar Calendar
for events the day of Tuesday, June 9, 2015.

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31

Tuesday, June 9, 2015

10:30 am in 347 Altgeld Hall,Tuesday, June 9, 2015

Noncommutative Stochastic Integration

Mathilde Perrin (ICMAT)

2:00 pm in 347 Altgeld Hall,Tuesday, June 9, 2015

Large BMO spaces and interpolation

Jose Conde (Barcelona)

Abstract: When one works in a von Neumann algebra $\mathcal{M}$ equipped with a filtration $\{\mathcal{M}_k\}_k$, if a BMO seminorm (not a norm) is defined by $$\|x\|_{BMO} = \sup_{k\geq 2} \|E_k|x-E_kx|^2 \|^{\frac12},$$ then the following interpolation identity holds: $$[BMO, L_1^\circ]_{1/p} = L_p^\circ.$$ Here $L_p^\circ$ is L_p modulo operators in $\mathcal{M}_1$. Sometimes, it is interesting to consider the situation when $\mathcal{M}_1$ is not trivial, ans then the interpolation result above may not be satisfactory. In this talk, we will explain how this is overcome in certain semicommutative scenarios and we will discuss the (wide open) situation of fully noncommutative algebras.