1,721,143 research outputs found
Unbounded derivations and *-automorphisms groups of Banach quasi *-algebras
Full text linkThis 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 are considered in a weak sense, i.e., with the use of a certain families of bounded sesquilinear forms. Conditions for a weak *-derivation to be the generator of a *-automorphisms group are given
Locally Convex Quasi *-Algebras and their Representations
No full textThis book is a review of the work the authors have done in the past 20 years on the theory of locally convex quasi *-algebra
Operator (Quasi-)Similarity, Quasi-Hermitian Operators and All that
No full textMotivated by the recent developments of pseudo-Hermitian quantum mechanics,
we analyze the structure generated by unbounded metric operators in a Hilbert
space. To that effect, we consider the notions of similarity and quasi-similarity between
operators and explore to what extent they preserve spectral properties. Then
we study quasi-Hermitian operators, bounded or not, that is, operators that are quasisimilar
to their adjoint and we discuss their application in pseudo-Hermitian quantum
mechanics. Finally, we extend the analysis to operators in a partial inner product
space (PIP-space), in particular the scale of Hilbert spaces generated by a single unbounded
metric operator.Motivated by the recent developments of pseudo-Hermitian quantum mechanics, we analyze the structure generated by unbounded metric operators in a Hilbert space. To that effect, we consider the notions of similarity and quasi-similarity between operators and explore to what extent they preserve spectral properties. Then we study quasi-Hermitian operators, bounded or not, that is, operators that are quasisimilar to their adjoint and we discuss their application in pseudo-Hermitian quantum mechanics. Finally, we extend the analysis to operators in a partial inner product space (pip-space), in particular the scale of Hilbert space s generated by a single unbounded metric operator
Dynamic Identification of a Solid Rocket Motor From Firing Test Using Operational Modal Analysis
No full textThe firing test of the first stage of the solid rocket motor P80 of the VEGA launcher was run successfully in December 2007 at the guyanese Space Center in Kourou. This research activity demonstrates the capability of the developed operational modal analysis methods to identify the dynamic properties of the solid rocket motor, working under its actual operative conditions, by using response data only recorded during the firing test. The main objective was first to prove the applicability and then to evaluate the overall efficiency of different state-of-the-art approaches in operational modal analysis to track changes in the natural frequencies, damping ratios and mode shapes of the first stage of the VEGA launch vehicle undergoing significant mass variation due to the burning propeller. Additionally, a sensitivity of the considered approaches to deal with structures characterized by time-dependent parameters was numerically carried out
Gibbs States, Algebraic Dynamics and Generalized Riesz Systems
Full text linkIn 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 if, most of the times, one is forced to deal with biorthogonal sets rather than with on orthonormal basis of eigenvectors. In this paper we consider some extended versions of the Heisenberg algebraic dynamics and we relate this analysis to some generalized version of Gibbs states and to their related KMS-like conditions. We also discuss some preliminary aspects of the Tomita–Takesaki theory in our context
Generalized Riesz Systems and Quasi Bases in Hilbert Space
Full text linkThe 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 { φn} and { ψn} , such that ∑n=0∞〈x,φn〉〈ψn,y〉=〈x,y〉 for all x∈ D and y∈ E. Second, it is shown that if biorthogonal sequences { φn} and { ψn} form a (D, E) -quasi basis, then they are generalized Riesz systems. The latter play an interesting role for the construction of non-self-adjoint Hamiltonians and other physically relevant operators
Maximal extensions of a linear functional
Full text linkExtensions of a positive hermitian linear functional ω, defined on a dense *-subalgebra A0 of a topological *-algebra A[τ] are analyzed. It turns out that their maximal extensions as linear functionals or hermitian linear functionals are everywhere defined. The situation however changes deeply if one looks for positive extensions. The case of fully positive and widely positive extensions considered in [2] is revisited from this point of view. Examples mostly taken from the theory of integration are discussed
Topological aspects of quasi *-algebras with sufficiently many *-representations
Full text linkQuasi *-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
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