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Nausica Aldeghi: Self-adjoint operators, quadratic forms and the Trotter product formula

Time: Fri 2019-11-15 13.00 - 14.00

Location: Kräftriket, house 5, room 32

Participating: Nausica Aldeghi, Stockholms universitet

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The well-known Lie product formula is a classic matrix theory result which allows to compare the product of the exponentials of two finite-dimensional matrices A, B with the exponential of their sum. Its proof, and therefore the formula itself, still hold for A, B bounded linear operators on a Hilbert space. It is natural to wonder if an analogous estimate holds for A, B unbounded linear operators on a Hilbert space.

In this talk we present progressive generalisations of the Lie product formula to infinite-dimensional cases, starting from the first product formula by Trotter (1959) and arriving to the most general result possible, due to Kato (1978). Since exponential and sum are the objects appearing in Lie product formula, in order to carry this generalisation out we will identify the class of unbounded operators which can be exponentiated and we will understand which sense should be given to the sum operation within this class. We will see how, in order to proceed, it is ultimately necessary to replace operators with quadratic forms.