The Positive Supercyclicity Theorem.
We present some recent results related with supercyclic operators, also some of its consequences. We will finalize with new related questions.
The product of relatively regular operators
The Projection onto the Center of Operators in a Banach Lattice.
The Quantum Birkhoff Normal Form and Spectral Asymptotics
In this talk we explain a simple treatment of the quantum Birkhoff normal form for semiclassical pseudo-differential operators with smooth coefficients. The normal form is applied to describe the discrete spectrum in a generalised non-degenerate potential well, yielding uniform estimates in the energy . This permits a detailed study of the spectrum in various asymptotic regions of the parameters , and gives improvements and new proofs for many of the results in the field. In the completely resonant...
The quasi-canonical solution operator to restricted to the Fock-space
We consider the solution operator to the -operator restricted to forms with coefficients in . Here denotes -forms with coefficients in , is the corresponding -space and is a suitable rotation-invariant absolutely continuous finite measure. We will develop a general solution formula to . This solution operator will have the property . As an application of the solution formula we will be able to characterize compactness of the solution operator in terms of compactness of commutators...
The Radon--Nikodym theorem for reflexive Banach spaces.
The range of a derivation on a Jordan-Banach algebra
The questions when a derivation on a Jordan-Banach algebra has quasi-nilpotent values, and when it has the range in the radical, are discussed.
The range of Toeplitz operators on the ball.
The rate of convergence of iterates of the Frobenius-Perron operator for piecewise monotonic transformations
The Regularized Trace for Nuclear Perturbations of Discrete Operators
The Schur multiplication in tensor algebras
The S...-criterion for Hankel forms on the Fock space, 0 < p < 1.
The second dual spaces of the sets of -strongly convergent and bounded sequences.
The set of automorphisms of B(H) is topologically reflexive in B(B(H))
The aim of this paper is to prove the statement announced in the title which can be reformulated in the following way. Let H be a separable infinite-dimensional Hilbert space and let Φ: B(H) → B(H) be a continuous linear mapping with the property that for every A ∈ B(H) there exists a sequence of automorphisms of B(H) (depending on A) such that . Then Φ is an automorphism. Moreover, a similar statement holds for the set of all surjective isometries of B(H).
The single-valued extension property and subharmonicity.
The single-valued extension property for sums and products of commuting operators
It is shown that the sum and the product of two commuting Banach space operators with Dunford’s property have the single-valued extension property.
The singular sequence problem
The solution by iteration of a composed K-positive definite operator equation in a Banach space.
The solution of the Kato problem in two dimensions.
We solve, in two dimensions, the "square root problem of Kato". That is, for L ≡ -div (A(x)∇), where A(x) is a 2 x 2 accretive matrix of bounded measurable complex coefficients, we prove that L1/2: L12(R2) → L2(R2).[Proceedings of the 6th International Conference on Harmonic Analysis and Partial Differential Equations, El Escorial (Madrid), 2002].
The Spectra of Hyponormal Integral Operators