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pro vyhledávání: '"TRAPANI, Camillo"'
The representations that can be defined starting from positive sesquilinear maps {\Phi} with values in an ordered Banach module are essentially of two types: if {\Phi} is positive, a natural generalization follows the path of the GNS construction; if
Externí odkaz:
http://arxiv.org/abs/2410.24113
It is known that the momentum operator canonically conjugated to the position operator for a particle moving in some bounded interval of the line {(with Dirichlet boundary conditions) is not essentially self-adjoint}: it has a continuous set of self-
Externí odkaz:
http://arxiv.org/abs/2406.06989
Publikováno v:
Mediterranean Journal of Mathematics (2024)
The GNS construction for positive invariant sesquilinear forms on quasi *-algebras is generalized to a class of positive C*-valued sesquilinear maps on quasi *-algebras. The result is a *-representation taking values in a space of operators acting on
Externí odkaz:
http://arxiv.org/abs/2403.16597
Autor:
Bellomonte, Giorgia, Trapani, Camillo
Quasi *-algebras possessing a sufficient family $\mathcal{M}$ of invariant positive sesquilinear forms carry several topologies related to $\mathcal{M}$ which make every *-representation continuous. This leads to define the class of locally convex qu
Externí odkaz:
http://arxiv.org/abs/2304.05725
After reviewing the interplay between frames and lower semi-frames, we introduce the notion of lower semi-frame controlled by a densely defined operator $A$ or, for short, a \emph{weak lower $A$-semi-frame} and we study its properties. In particular,
Externí odkaz:
http://arxiv.org/abs/2012.09101
In PT-quantum mechanics the generator of the dynamics of a physical system is not necessarily a self-adjoint Hamiltonian. It is now clear that this choice does not prevent to get a unitary time evolution and a real spectrum of the Hamiltonian, even i
Externí odkaz:
http://arxiv.org/abs/2009.02950
The purpose of this article is twofold. First of all, the notion of $(D, E)$-quasi basis is introduced for a pair $(D, E)$ of dense subspaces of Hilbert spaces. This consists of two biorthogonal sequences $\{ \varphi_n \}$ and $\{ \psi_n \}$ such tha
Externí odkaz:
http://arxiv.org/abs/1907.05604
Akademický článek
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In this paper we will consider, in the abstract setting of rigged Hilbert spaces, distribution valued functions and we will investigate, in particular, conditions for them to constitute a "continuous basis" for the smallest space $\mathcal D$ of a ri
Externí odkaz:
http://arxiv.org/abs/1812.08472
Autor:
Adamo, Maria Stella, Trapani, Camillo
This paper is devoted to the study of unbounded derivations on Banach quasi *-algebras with a particular emphasis to the case when they are infinitesimal generators of one parameter automorphisms groups. Both of them, derivations and automorphisms ar
Externí odkaz:
http://arxiv.org/abs/1807.11525