757 research outputs found
Semicrossed products generated by two commuting automorphisms
We study the semicrossed product of a finite dimensional C^*-algebra by two
types of commuting automorphisms, and identify them with matrix algebras of
analytic functions in two variables. We look at the connections with
semicrossed products by Z_+ actions.Comment: 15 page
Meet Irreducible Ideals and Representations of Limit Algebras
In this paper we give a criterion for an ideal of a TAF algebra to be meet
irreducible. We show that an ideal of is meet irreducile if and only if
the C-envelope of the quotient is primitive. In that case, A/J admits
a nest representation which extends to a *-representation of the C-envelope
for We also characterize the meet irreducible ideals as the kernels of
nest representations; this settles the question of whether the n-primitive and
meet irreducible ideals coincide.Comment: 8 pages; accepted in JF
Singly Generated Radical Operator Algebras
We examine two nonselfadjoint operator algebras: the weighted shift algebra,
and the Volterra operator algebra. In both cases, the operator algebra is the
norm closure of the polynomials in the operator norm. In the case of the
weighted shift algebra, the existence of a gauge action allows us to apply
Fourier analysis to study the ideals of the algebra. In the case of the
Volterra operator algebra, there is no gauge action, and other methods are
needed to study the norm structure and the ideals
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