Search results for "Compact"

Transformations by diagonal matrices in a normed space

1962

Ergodic properties of operators in some semi-Hilbertian spaces

2012

This article deals with linear operators T on a complex Hilbert space ℋ, which are bounded with respect to the seminorm induced by a positive operator A on ℋ. The A-adjoint and A 1/2-adjoint of T are considered to obtain some ergodic conditions for T with respect to A. These operators are also employed to investigate the class of orthogonally mean ergodic operators as well as that of A-power bounded operators. Some classes of orthogonally mean ergodic or A-ergodic operators, which come from the theory of generalized Toeplitz operators are considered. In particular, we give an example of an A-ergodic operator (with an injective A) which is not Cesaro ergodic, such that T  * is not a quasiaff…

Metric operators, generalized hermiticity and partial inner product spaces

2015

A quasi-Hermitian operator is an operator in a Hilbert space that is similar to its adjoint in some sense, via a metric operator, i.e., a strictly positive self-adjoint operator. Motivated by the recent developments of pseudo-Hermitian quantum mechanics, we analyze the structure of metric operators, bounded or unbounded, in a Hilbert space. We introduce several generalizations of the notion of similarity between operators and explore to what extent they preserve spectral properties. Next we consider canonical lattices of Hilbert spaces generated by unbounded metric operators. Since such lattices constitute the simplest case of a partial inner product space (PIP space), we can exploit the te…

Metric Operators, Generalized Hermiticity and Lattices of Hilbert Spaces

2015

Pseudo-Hermitian quantum mechanics (QM) is a recent, unconventional, approach to QM, based on the use of non-self-adjoint Hamiltonians, whose self-adjointness can be restored by changing the ambient Hilbert space, via a so-called metric operator. The PT-symmetric Hamiltonians are usually pseudo-Hermitian operators, a term introduced a long time ago by Dieudonné for characterizing those bounded operators A that satisfy a relation of the form GA = A G, where G is a metric operator, that is, a strictly positive self-adjoint operator. This chapter explores further the structure of unbounded metric operators, in particular, their incidence on similarity. It examines the notion of similarity betw…

Completeness number of families of subsets of convergence spaces

2016

International audience; Compactoid and compact families generalize both convergent filters and compact sets. This concept turned out to be useful in various quests, like Scott topologies, triquotient maps and extensions of the Choquet active boundary theorem.The completeness number of a family in a convergence space is the least cardinality of collections of covers for which the family becomes complete. 0-completeness amounts to compactness, finite completeness to relative local compactness and countable completeness to Čech completeness. Countably conditional countable completeness amounts to pseudocompleteness of Oxtoby. Conversely, each completeness class of families can be represented a…

Elements with square roots in compact groups

2010

The probability that a randomly chosen element has a square root is studied in [1, 2, 8] in the finite case. Here we deal with the infinite case.

High Order Compact Finite Difference Schemes for A Nonlinear Black-Scholes Equation

2001

A nonlinear Black-Scholes equation which models transaction costs arising in the hedging of portfolios is discretized semi-implicitly using high order compact finite difference schemes. A new compact scheme, generalizing the compact schemes of Rigal [29], is derived and proved to be unconditionally stable and non-oscillatory. The numerical results are compared to standard finite difference schemes. It turns out that the compact schemes have very satisfying stability and non-oscillatory properties and are generally more efficient than the considered classical schemes.

Deformation of melt-bearing systems—insight from in situ grain-scale analogue experiments

2005

Abstract The deformation behaviour of partially molten rocks was investigated using in situ analogue experiments with norcamphor+ethanol, as well as partially molten KNO 3 +LiNO 3 . Three general deformation regimes could be distinguished during bulk pure shear deformation. In regime I, above ca. 8–10 vol.% liquid (melt) fraction ( ϕ bulk ), deformation is by compaction, distributed granular flow, and grain boundary sliding (GBS). At ϕ bulk ϕ bulk (regime III), grains form a coherent framework that deforms by grain boundary migration accommodated dislocation creep, associated with efficient segregation of remaining liquid. The transition liquid fraction between regimes I and II ( ϕ LT ) dep…

Form-perturbation theory for higher-order elliptic operators and systems by singular potentials

2020

We give a form-perturbation theory by singular potentials for scalar elliptic operators onL2(Rd)of order 2mwith Hölder continuous coefficients. The form-bounds are obtained from anL1functional analytic approach which takes advantage of both the existence ofm-gaussian kernel estimates and the holomorphy of the semigroup inL1(Rd).We also explore the (local) Kato class potentials in terms of (local) weak compactness properties. Finally, we extend the results to elliptic systems and singular matrix potentials.This article is part of the theme issue ‘Semigroup applications everywhere’.

Dopaminergic control of feline hippocampal epilepsy: A nigrophippocampal pathway

1991

Abstract Substantia nigra is a mesencephalic structure inserted along several circuits which appear to play a key role in epilepsy. In previous researches we postulated that substantia nigra pars compacta (SNpc) may be the site of a precise control of hippocampal epilepsy while substantia nigra pars reticulata (SNpr) may exert a modulation of both neocortical epilepsy and spreading of hyperactivity toward a motor target. In order to better understand mechanisms subserving nigral action in feline hippocampal epilepsy we electrically stimulated SNpc (dopaminergic), before and after sulpiride (dopamine receptor-antagonist) intravenous injection. Furthermore we compared hippocampal epileptiform…