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Finite-dimensional Lie subalgebras of algebras with continuous inversion

Daniel Beltiţă, Karl-Hermann Neeb (2008)

Studia Mathematica

We investigate the finite-dimensional Lie groups whose points are separated by the continuous homomorphisms into groups of invertible elements of locally convex algebras with continuous inversion that satisfy an appropriate completeness condition. We find that these are precisely the linear Lie groups, that is, the Lie groups which can be faithfully represented as matrix groups. Our method relies on proving that certain finite-dimensional Lie subalgebras of algebras with continuous inversion commute...

Fonctions analytiques de contractions topologiques dans les algèbres hermitiennes.

Abdellah El Kinani (1990)

Collectanea Mathematica

In this paper we define a functional calculus, for harmonic vector valued functions, in Banach algebras with continuous involution. Using this calculus, we generalize in two settings the results of Shih and Tan on analytic functions of topological proper contractions to analytic vector valued functions in Hermitian Banach algebras. We also make an extension of other results such as Schwarz's lemma and Pick's theorem.

Fonctions harmoniques opérant sur les algèbres de Banach involutives

Abdellah Elkinani (1991)

Annales de l'institut Fourier

Nous introduisons un calcul fonctionnel pour les fonctions harmoniques sur un ouvert du plan complexe et à valeurs dans une algèbre de Banach à involution continue. Ensuite, nous donnons dans les algèbres hermitiennes deux extensions des théorèmes de von Neumann et de Ky Fan sur les contractions. Nous obtenons également les analogues du lemme de Schwarz et du théorème de Pick.

Function theory in sectors

Brian Jefferies (2004)

Studia Mathematica

It is shown that there is a one-to-one correspondence between uniformly bounded holomorphic functions of n complex variables in sectors of ℂⁿ, and uniformly bounded functions of n+1 real variables in sectors of n + 1 that are monogenic functions in the sense of Clifford analysis. The result is applied to the construction of functional calculi for n commuting operators, including the example of differentiation operators on a Lipschitz surface in n + 1 .

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