| 11. |
- Aleman, Alexandru, et al.
(author)
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Recent progress and open problems in the Bergman space.
- 2005
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In: Oper. Theory Adv. Appl.Operator Theory: Advances and Applications.. ; 156, s. 27-59
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Journal article (peer-reviewed)abstract
- The aim of this work is to provide a survey of interesting open problems in the theory of Bergman spaces
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| 12. |
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| 13. |
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| 14. |
- Aleman, Alexandru, et al.
(author)
-
Uniform spectral radius and compact Gelfand transform
- 2006
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In: Studia Mathematica. - 0039-3223. ; 172:1, s. 25-46
-
Journal article (peer-reviewed)abstract
- We consider the quantization of inversion in commutative p-normed quasi-Banach algebras with unit. The standard questions considered for such an algebra A with unit e and Gelfand transform x bar right arrow (x) over cap are: (i) Is K-nu = sup{parallel to(e - x)(-1)parallel to(p) : x is an element of A, parallel to x parallel to(p) <= 1, max (x) over cap <= nu} bounded, where nu is an element of (0, 1)? (ii) For which delta is an element of (0, 1) is C-delta = sup{parallel to x(-1)parallel to(p) : x is an element of A, parallel to x parallel to(p) <= 1, min (x) over cap >= delta} bounded? Both questions are related to a "uniform spectral radius" of the algebra, r(infinity)(A), introduced by Bjork. Question (i) has an affirmative answer if and only if r(infinity)(A) < 1, and this result is extended to more general nonlinear extremal problems of this type. Question (ii) is more difficult, but it can also be related to the uniform spectral radius. For algebras with compact Gelfand transform we prove that the answer is "yes" for all delta is an element of (0, 1) if and only if r(infinity)(A) = 0. Finally, we specialize to semisimple Beurling type algebras l(w)(p)(D), where 0 < p < 1 and D = N or D = Z. We show that the number r(infinity)(l(w)(p)(D)) can be effectively computed in terms of the underlying weight. In particular, this solves questions (i) and (ii) for many of these algebras. We also construct weights such that the corresponding Beurling algebra has a compact Gelfand transform, but the uniform spectral radius equals an arbitrary given number in (0, 1].
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| 15. |
- Aleman, Alexandru, et al.
(author)
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Volterra invariant subspaces of H-p
- 2008
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In: Bulletin des Sciences Mathématiques. - : Elsevier BV. - 0007-4497. ; 132:6, s. 510-528
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Journal article (peer-reviewed)abstract
- A complete description is obtained for the subspaces of the Hardy space H-P (p >= 1) that are invariant under the Volterra integral operator. We then show that this result can be applied to derive complete characterizations of such subspaces in a large class of Banch spaces of analytic functions in the unit disc containing the usual Bergman and Dirichlet spaces. (C) 2007 Elsevier Masson SAS. All rights reserved.
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| 16. |
- Aleman, Alexandru, et al.
(author)
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Zero products of Toeplitz operators
- 2009
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In: Duke Mathematical Journal. - : Duke University Press. - 0012-7094. ; 148:3, s. 373-403
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Journal article (peer-reviewed)abstract
- We prove that the product of finitely many Toeplitz operators oil the Hardy space is zero if and only if at least one of the operators is zero. We use some new vector-valued techniques that not only lead to a vector-valued version of this result but also appear to be needed in the scalar case.
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