Search results for " Opera"
showing 10 items of 3606 documents
A bounded version of bosonic creation and annihilation operators and their related quasi-coherent states
2007
Coherent states are usually defined as eigenstates of an unbounded operator, the so-called annihilation operator. We propose here possible constructions of {\em quasi-coherent states}, which turn out to be {\em quasi} eigenstate of a \underline{bounded} operator related to an annihilation-like operator. We use this bounded operator to construct a sort of modified harmonic oscillator and we analyze the dynamics of this oscillator from an algebraic point of view.
Weyl's theorem for perturbations of paranormal operators
2007
A bounded linear operator T ∈ L(X) on a Banach space X is said to satisfy "Weyl's theorem" if the complement in the spectrum of the Weyl spectrum is the set of all isolated points of the spectrum which are eigenvalues of finite multiplicity. In this paper we show that if T is a paranormal operator on a Hilbert space, then T + K satisfies Weyl's theorem for every algebraic operator K which commutes with T.
Existence theorems for inclusions of the type
1999
For a family of operator inclusions with convex closed-valued right-hand sides in Banach spaces, the existence of solutions is obtained by chiefly using Ky Fan's fixed point principle. The main result of the paper improves Theorem 1 in [16] as well as Theorem 2.2 of [3]. Some meaningful concrete cases are also presented and discussed.
Refinements of PIP-Spaces
2009
We have seen in Section 1.5, that the compatibility relation underlying a pip-space may always be coarsened, but not refined in general. There is an exception, however, namely the case of a scale of Hilbert spaces and analogous structures. We shall describe it in this section.
Partial O*-Algebras
2002
This chapter is devoted to the investigation of partial O*-algebras of closable linear operators defined on a common dense domain in a Hilbert space. Section 2.1 introduces of O- and O*-families, O- and O*-vector spaces, partial O*-algebras and O*-algebras. Partial O*-algebras and strong partial O*-algebras are defined by the weak and the strong multiplication. Section 2.2 describes four canonical extensions (closure, full-closure, adjoint, biadjoint) of O*-families and defines the notions of closedness and full-closedness (self-adjointness, integrability) of O*-families in analogy with that of closed (self-adjoint) operators. Section 2.3 deals with two weak bounded commutants M′w and M′qw …
Spectra and essential spectral radii of composition operators on weighted Banach spaces of analytic functions
2008
AbstractWe determine the spectra of composition operators acting on weighted Banach spaces Hv∞ of analytic functions on the unit disc defined for a radial weight v, when the symbol of the operator has a fixed point in the open unit disc. We also investigate in this case the growth rate of the Koenigs eigenfunction and its relation with the essential spectral radius of the composition operator.
Physical oceanography, sea-bed photographs and videos of benthos from the Weddell Sea taken with remote operated vehicle CHEROKEE during POLARSTERN c…
2010
The marine ecosystem on the eastern shelf of the Antarctic Peninsula was surveyed 5 and 12 years after the climate-induced collapse of the Larsen A and B ice shelves. An impoverished benthic fauna was discovered, that included deep-sea species presumed to be remnants from ice-covered conditions. The current structure of various ecosystem components appears to result from extremely different response rates to the change from an oligotrophic sub-ice-shelf ecosystem to a productive shelf ecosystem. Meiobenthic communities remained impoverished only inside the embayments. On local scales, macro- and mega-epibenthic diversity was generally low, with pioneer species and typical Antarctic megabent…
Operator martingale decomposition and the Radon-Nikodym property in Banach spaces
2010
Abstract We consider submartingales and uniform amarts of maps acting between a Banach lattice and a Banach lattice or a Banach space. In this measure-free setting of martingale theory, it is known that a Banach space Y has the Radon–Nikodým property if and only if every uniformly norm bounded martingale defined on the Chaney–Schaefer l-tensor product E ⊗ ˜ l Y , where E is a suitable Banach lattice, is norm convergent. We present applications of this result. Firstly, an analogues characterization for Banach lattices Y with the Radon–Nikodým property is given in terms of a suitable set of submartingales (supermartingales) on E ⊗ ˜ l Y . Secondly, we derive a Riesz decomposition for uniform …
The Average State Complexity of the Star of a Finite Set of Words Is Linear
2008
We prove that, for the uniform distribution over all sets Xof m(that is a fixed integer) non-empty words whose sum of lengths is n, $\mathcal{D}_X$, one of the usual deterministic automata recognizing X*, has on average $\mathcal{O}(n)$ states and that the average state complexity of X*is i¾?(n). We also show that the average time complexity of the computation of the automaton $\mathcal{D}_X$ is $\mathcal{O}(n\log n)$, when the alphabet is of size at least three.
The Daugavet equation for polynomials
2007
In this paper we study when the Daugavet equation is satisfied for weakly compact polynomials on a Banach space X, i.e. when the equality ‖Id + P‖ = 1 + ‖P‖ is satisfied for all weakly compact polynomials P : X −→ X. We show that this is the case when X = C(K), the real or complex space of continuous functions on a compact space K without isolated points. We also study the alternative Daugavet equation max |ω|=1 ‖Id + ω P‖ = 1 + ‖P‖ for polynomials P : X −→ X. We show that this equation holds for every polynomial on the complex space X = C(K) (K arbitrary) with values in X. The result is not true in the real case. Finally, we study the Daugavet and the alternative Daugavet equations for k-h…