1,720,970 research outputs found
The eigenvalues of limits of radial Toeplitz operators
Full text linkLet A2 be the Bergman space on the unit disk. A bounded operator S on A2 is called radial if Szn = λnzn for all n 0, where λn is a bounded sequence of complex numbers. We characterize the eigenvalues of radial operators that belong to the Toeplitz algebra.Fil: Suarez, Fernando Daniel. Universitat Autònoma de Barcelona; España. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; Argentin
A counterexample for H ∞ approximable functions
Full text linkLet D be the unit disk. We show that for some relatively closed set F ⊂ D there is a function f that can be uniformly approximated on F by functions of H∞, but such that f cannot be written as f = h + g, with h ∈ H∞ and g uniformly continuous on F. This answers a question of Stray.Fil: Suarez, Fernando Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentin
Localisation techniques for division in Douglas algebras
Full text linkIn this paper we use uniform algebra techniques and recent results on separation properties to prove several division theorems for closed subalgebras of L∞ containing H∞. We also study ideals having the local approximation property and we show that not every ideal in such algebras is local.Fil: Suarez, Fernando Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentin
The Toeplitz algebra on the Bergman space coincides with its commutator ideal
Full text linkLet L^2-a be the Bergman space of the unit disk and T(L^2_a) be the Banach algebra generated by Toeplitz operators T_f , with f ∈ L∞. We prove that the closed bilateral ideal of T(L2a) generated by operators of the form T_fT_g − T_gT_f coincides with T(L^2_a).Fil: Suarez, Fernando Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentin
On the stable rank of Q p ∩ H ∞
Full text linkLet 0 0, there exists g in Q p ∩ H ∞ such that f 1 + gf 2 is invertible in Q p ∩ H ∞. As a partial answer to this problem, we prove the result when f 1 is an inner function in Q p .Fil: Pau, Jordi. Universidad de Barcelona; EspañaFil: Suarez, Fernando Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; Argentina. Universitat Autònoma de Barcelona; Españ
The Essential Norm of Operators in the Toeplitz Algebra on Ap(Bn)
Full text linkLet Ap be the Bergman space on the unit ball Bn of Cn for 1 <p< ∞, and Tp be the corresponding Toeplitz algebra. We show that every S ∈ Tp can be approximated by operators that are specially suited for the study of local behavior. This is used to obtain several estimates for the essential norm of S ∈ Tp, an estimate for the essential spectral radius of S ∈ T2, and a localization result for its essential spectrum. Finally, we characterize compactness in terms of the Berezin transform for operators in Tp.Fil: Suarez, Fernando Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; Argentin
Approximation and the n-Berezin transform of operators on the Bergman space
Full text linkTo any bounded operator S on the Bergman space La2 we associate a sequence of linear transforms Bn(S ) ∈ L∞(D), where n ≧ 0, and prove that the Toeplitz operators article image tend to S for some especial classes of operators S. In particular, this holds for every radial operator in the Toeplitz algebra. Finally, we show that the inclusion of the Toeplitz algebra into the essential commutant of the Bergman shift is proper.Fil: Suarez, Fernando Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universitat Autònoma de Barcelona; Españ
On the analytic structure of the H∞ maximal ideal space
Full text linkWe characterize the algebra H∞ ◦L_m, where m is a point of the maximal ideal space of H∞ with nontrivial Gleason part P(m) and L_m : D→P(m) is the coordinate Hoffman map. In particular, it is shown that for any continuous function f : P(m)→C with f ◦L_m ∈ H∞ there exists F ∈ H∞ such that F|_P(m) = f.Fil: Suarez, Fernando Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentin
An upper bound for the distance to finitely generated ideals in Douglas algebras
Full text linkLet f be a function in the Douglas algebra A and let I be a finitely generated ideal in A. We give an estimate for the distance from f to I that allows us to generalize a result obtained by Bourgain for H∞ to arbitrary Douglas algebras.Fil: Gorkin, Pamela. No especifíca;Fil: Mortini, Raymond. No especifíca;Fil: Suarez, Fernando Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentin
Norm closed invariant subspaces in H∞ and L∞
Full text linkWe characterize norm closed subspaces B of L∞(∂D) such that C(∂D)B ⊂ B, and maximal ones in the family of proper closed subspaces B of L∞(∂D) such that A(D)B ⊂ B, where A(D) is the disk algebra. Analogously, we characterize closed subspaces of H∞ that are simultaneously invariant under S and S∗, the forward and the backward shift operators, and maximal invariant subspaces of H∞.Fil: Suarez, Fernando Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaFil: IzuchiI, Keiji. Niigata University; Japó
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