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Representations of Polish groups and continuity

M. Cianfarani, J.-M. Paoli, P. Simonnet, J.-C. Tomasi (2014)

Studia Mathematica

In the first part of the paper, some criteria of continuity of representations of a Polish group in a Banach algebra are given. The second part uses the result of the first part to deduce automatic continuity results of Baire morphisms from Polish groups to locally compact groups or unitary groups. In the final part, the spectrum of an element in the range of a strongly but not norm continuous representation is described.

Resolvent and spectrum of a nonselfadjoint differential operator in a Hilbert space

Michael Gil (2012)

Annales UMCS, Mathematica

We consider a second order regular differential operator whose coefficients are nonselfadjoint bounded operators acting in a Hilbert space. An estimate for the resolvent and a bound for the spectrum are established. An operator is said to be stable if its spectrum lies in the right half-plane. By the obtained bounds, stability and instability conditions are established.

Resolvent conditions and powers of operators

Olavi Nevanlinna (2001)

Studia Mathematica

We discuss the relation between the growth of the resolvent near the unit circle and bounds for the powers of the operator. Resolvent conditions like those of Ritt and Kreiss are combined with growth conditions measuring the resolvent as a meromorphic function.

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