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Algebras in Analysis
November 15, 2019 18:05–19:35, Moscow, Lomonosov Moscow State University, room 13-20.

On a generator of the semigroup of shifts on the algebra of canonical anticommutation relations

G. G. Amosov

Abstract: Let $S_t=e^{td}, t\ge 0$ be a one-parameter semigroup of isometrical operators in a Hilbert space $H$ which is continuous in strong operator topology and $d$ be its generator with the dense domain $D(d)$. Then,
$$\alpha _t(x)=S_t^*xS_t, t\ge 0,$$
$x\in B(H)$, is a semigroup of (non-unital in general) *-endomorphisms of the algebra of all bounded operators $B(H)$ with the generator
$$\delta (x)=d^*x+xd,$$
$x\in D(\delta )$. It will be shown how applying a singular perturbation of $\delta$ it is possible to obtain the generator and the equation for the semigroup of shifts on the algebra of canonical anticommutation relations in the antisymmetric Fock space.