Advanced Course in Operator Theory and Complex Analysis (1st. 2004. Sevilla)
Recent Submissions

On the growth of Hardy and Bergman norms of functions in the Dirichlet space [Presentation]
(Editorial Universidad de Sevilla, 2005)We review the ChangMarshall inequality of MoserTrudinger 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 ...

On spectral structure of bounded linear operators on reflexive Banach spaces [Presentation]
(Editorial Universidad de Sevilla, 2005)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 ...

Composition operators on the weighed BergmanNevanlinna classes [Presentation]
(Editorial Universidad de Sevilla, 2005)In this paper we use an αCarleson measure and a vanishing Carleson measure to characterize bounded and compact composition operators on weighted BergmanNevanlinna spaces.

Operators on Lp and the role of the image of the unit ball [Presentation]
(Editorial Universidad de Sevilla, 2005)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 ...

Composition operators with linear fractional smbols and their adjoints [Presentation]
(Editorial Universidad de Sevilla, 2005)We characterize all linear fractional maps of the disk into itself in terms of their coefficients. We also prove the formula for the adjoint of a composition operator with a linear fractional symbol acting on the quotient ...

Toeplitz operators and division by inner functions [Presentation]
(Editorial Universidad de Sevilla, 2005)A subspace X of the Hardy space H1 is said to have the Kproperty if for any ψ ∈ H∞, the Toeplitz operator Tψ maps X into itself. This in turn implies that X also has the fproperty. This means that h/I ∈ X whenever h ∈ X ...

Banach algebras with trivial cohomology [Presentation]
(Editorial Universidad de Sevilla, 2005)A plausible conjecture is that Banach algebras with trivial cohomology have to be semisimple and finite dimensional. In this paper, we show that a Hermitian Banach ∗algebra has trivial cohomology if and only if it is ...

A parametrization for the symbols of a Hankel type operator [Presentation]
(Editorial Universidad de Sevilla, 2005)Hankel operators and their symbols, as generalized by V. Pták and P. Vrbová, are considered. In this more general framework, a linear operator X from a Hilbert space H1 to a Hilbert space H2 is said to be a Hankel operator ...

Volterra operators on spaces of analytic functions  a survey [Presentation]
(Editorial Universidad de Sevilla, 2005)We give a short and selective account of results known about operators of the form Vg(f)(z) = 1/z Z z 0 f(ζ)g0 (ζ) dζ, where g is analytic on the disc and the operator Tg = zVg acts on spaces of analytic functions.

Invariant subspaces of translation semigroups [Presentation]
(Editorial Universidad de Sevilla, 2005)In these lectures I shall give an account of some recent results and open problems relating to subspaces of square integrable functions on the real line which are jointly invariant for a pair of semigroups of unitary ...

How large is a Riemann surface: the type problem [Presentation]
(Editorial Universidad de Sevilla, 2005)The uniformization theorem asserts that a simplyconnected noncompact Riemann surface S is conformally equivalent to precisely one of the unit disk D or the finite complex plane C. While this result (nearly a century old) ...

Analytic contractions and boundary behaviour  an overview [Presentation]
(Editorial Universidad de Sevilla, 2005)