

Algebras in Analysis
November 15, 2019 18:05–19:35, Moscow, Lomonosov Moscow State University, room 1320.






On a generator of the semigroup of shifts on the algebra of canonical anticommutation relations
G. G. Amosov^{} 
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Abstract:
Let $S_t=e^{td}, t\ge 0$ be a oneparameter 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 (nonunital 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.

