32 research outputs found
Operators in Rigged Hilbert spaces: some spectral properties
A notion of resolvent set for an operator acting in a rigged Hilbert space
\D \subset \H\subset \D^\times is proposed. This set depends on a family of
intermediate locally convex spaces living between \D and \D^\times, called
interspaces. Some properties of the resolvent set and of the corresponding
multivalued resolvent function are derived and some examples are discussed.Comment: 29 page
Fully representable and *-semisimple topological partial *-algebras
We continue our study of topological partial *-algebras, focusing our
attention to *-semisimple partial *-algebras, that is, those that possess a
{multiplication core} and sufficiently many *-representations. We discuss the
respective roles of invariant positive sesquilinear (ips) forms and
representable continuous linear functionals and focus on the case where the two
notions are completely interchangeable (fully representable partial *-algebras)
with the scope of characterizing a *-semisimple partial *-algebra. Finally we
describe various notions of bounded elements in such a partial *-algebra, in
particular, those defined in terms of a positive cone (order bounded elements).
The outcome is that, for an appropriate order relation, one recovers the
\M-bounded elements introduced in previous works.Comment: 26 pages, Studia Mathematica (2012) to appea
Topological aspects of quasi *-algebras with sufficiently many *-representations
Quasi *-algebras possessing a sufficient family M of invariant positive sesquilinear forms carry several topologies related to M which make every *-representation continuous. This leads to define the class of locally convex quasi GA*-algebras whose main feature consists in the fact that the family of their bounded elements, with respect to the family M, is a dense C*-algebra
Disequazioni variazionali, problemi di ottimo e convessita' generalizzata
Il lavoro fatto nella tesi propone un'estensione dei principali teoremi sulle disequazioni variazionali vettoriali (VVI), considerando l'ordinamento indotto da un generico cono C di R^p (convesso, chiuso, puntato e con interno non vuoto) anziche' dal classico cono d'ordine R^p_+ . Uno dei principali risultati e' l'estensione di un risultato in [2], che lega le VVI ad una famiglia di disequazioni variazionali scalari dipendenti da un parametro. Da esso seguono alcuni dei principali teoremi di esistenza mediante il riconducimento al caso scalare. Il risultato, inoltre, insieme ad opportune ipotesi di C-convessita' generalizzata sulla funzione obiettivo, garantisce l'esistenza di soluzioni per problemi di ottimo vettoriale.
Il lavoro si conclude con le dimostrazioni di due nuove condizioni sufficienti di buona posizione per una disequazione variazionale vettoriale debole (nel seguito VVI^w) il cui operatore ammette primitiva. La prima amplia la classe delle funzioni per cui viene garantita la buona posizione di VVI^w(X, Jf ), facendo uso dell'ipotesi di C-pseudo- convessit'a per la funzione f , anziche' di quella di C-convessit'a. L'altra condizione, oltre a far uso di quest'ipotesi piu' debole su f , richiede la connessione di alcuni insiemi coinvolti nella definizione di buona posizione e la limitatezza dell'insieme delle soluzioni del problema di ottimo vettoriale debole (nel seguito VOP^w). Da tali risultati sono poi dedotte altrettante condizioni sufficienti per la buona posizione di VOP^w( f , X)
Pedagogical Models Of Surface Mechanical Wave Propagation In Various Materials
We report on a teaching approach oriented to the understanding of some relevant concepts of wave propagation in solids. It is based on simple experiments involving the propagation of shock mechanical waves in solid slabs of various materials. Methods similar to the generation and propagation of seismic waves are adopted. Educational seismometers, interfaced with computers, are used to detect and visualize the shock waves and to analyse their propagation properties. A qualitative discussion of the results concerning the propagation and the attenuation of the waves allows us to draw basic conclusions about the response of the matter to solicitation impacts and their propagation
An overview on bounded elements in some partial algebraic structures
The notion of bounded element is fundamental in the framework of the spectral theory. Before implanting a spectral theory in some algebraic or topological structure it is needed to establish which are its bounded elements. In this paper, we want to give an overview on bounded elements of some particular algebraic and topological structures, summarizing our most recent results on this matte