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ON THE JOINT SPECTRA OF THE TWO DIMENSIONAL LIE ALGEBRA OF OPERATORS IN HILBERT SPACES

By Union Matematica Argentina, Enrico Boas So and Buenos Aires

Abstract

ABSTRACT. We consider the complex solvable non-commutative two dimensional Lie algebra L, L =< Y> Ell < x>, with Lie bracket [x,y) = y, as linear bounded operators acting on a complex Hilbert space H. Under the assumption R(y) closed, we reduce the computation of the joint spectra Sp(L, E), U6,k(L, E) and u,..,k(L, E), k = 0,1,2, to the computation of the spectrum, the approximate point spectrum, and the approximate compression spectrum of a single operator. Besides, we also study the case y2 = = 0, and we apply our results to the case H finite dimensional 1. Introduction. In [1] we introduced a joint spectrum for complex solvable finite dimensional Lie algebras of operators acting on a Banach space E. If L is such an algebra, and Sp(L, E) denotes its joint spectrum, Sp(L, E) is a compact non empty subset o

Year: 2013
OAI identifier: oai:CiteSeerX.psu:10.1.1.297.6669
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