Advanced Course in Operator Theory and Complex Analysis (1st. 2004. Sevilla)
https://hdl.handle.net/11441/61375
2021-05-07T20:16:32ZOn the growth of Hardy and Bergman norms of functions in the Dirichlet space
https://hdl.handle.net/11441/61435
On the growth of Hardy and Bergman norms of functions in the Dirichlet space
Montes Rodríguez, Alfonso
We review the Chang-Marshall inequality of Moser-Trudinger type for the Dirichlet space. We then use a weaker version of this result to derive a sharp asymptotic estimate for Hardy and Bergman norms of a Dirichlet function for large exponents.
2005-01-01T00:00:00ZOn spectral structure of bounded linear operators on reflexive Banach spaces
https://hdl.handle.net/11441/61434
On spectral structure of bounded linear operators on reflexive Banach spaces
Montes Rodríguez, Alfonso
A descriptive characterization of point, continuous, and residual spectra of operators acting on a separable Hilbert space is obtained. The possible point spectra of bounded linear operators acting on lp, 1 < p < ∞ are characterized.
2005-01-01T00:00:00ZComposition operators on the weighed Bergman-Nevanlinna classes
https://hdl.handle.net/11441/61433
Composition operators on the weighed Bergman-Nevanlinna classes
Montes Rodríguez, Alfonso
In this paper we use an α-Carleson measure and a vanishing Carleson measure to characterize bounded and compact composition operators on weighted Bergman-Nevanlinna spaces.
2005-01-01T00:00:00ZOperators on Lp and the role of the image of the unit ball
https://hdl.handle.net/11441/61431
Operators on Lp and the role of the image of the unit ball
Montes Rodríguez, Alfonso
Let p ∈ [1, +∞] such that its conjugate exponent q is not an even integer and let T be an operator defined on Lp(λ) with values in a Banach space. In this note we discuss how the image of the unit ball determines whether T belongs to some classes of operators such as operator ideals or the class of representable operators. We also study the monotonicity of these properties, proving that a Banach space is Cisomorphic to a subspace of an Lq
space if and only if the representability of every operator on Lp is monotone with respect to the image of the unit ball.
2005-01-01T00:00:00Z