Weyl Spectrum Research Articles

Weyl's Theorem for Algebraically (\(\wp, \wr, \varrho\))-Paranormal and Algebraically (\(\wp, \wr, \varrho\))-*-Paranormal Operators

Present L be an algebraically (\(\wp, \wr, \varrho\))-Paranormal and algebraically (\(\wp, \wr, \varrho\))-*-Paranormal operators on \(L^2\) space. We examine Weyl's theorem, a-Browder's theorem and spectral mapping theorem holds for weyl's spectrum of L and essential approximate point spectrum of L.

Locating the spectrum of a relation matrix through those of its inputs

Let [Formula: see text] and [Formula: see text] be Banach spaces. When [Formula: see text] and [Formula: see text] are linear relations in [Formula: see text] and [Formula: see text], respectively, we denote by [Formula: see text] the linear relation matrix acting on [Formula: see text] of the form [Formula: see text], where [Formula: see text] is the zero operator and [Formula: see text] is a bounded operator from [Formula: see text] to [Formula: see text]. In this paper, we prove that if [Formula: see text] denotes the Weyl spectrum, the Browder spectrum or the Drazin spectrum of a linear relation, then for every [Formula: see text] we have the equality [Formula: see text] where [Formula: see text] a subset of [Formula: see text]. Moreover, we explore how Weyl’s theorem and Browder’s theorem hold for linear relation matrices.

The quasi-similarity and dominant conditions of Weyl spectrum in a complex Hilbert space

The study of spectrum in Hilbert spaces is a very rich in giving more structures of the spectrum and we wish to go in to depth to understand deeper on the structure of the spectrum. Apart from the well-known components of spectrum i.e. spectrum, the approximate point spectrum, the point spectrum and the set of eigenvalues of finite multiplicity: there is need for further study on the Weyl spectrum of an Operator in a complex Hilbert space. To succeed in this study, two conditions to help expose properties of the Weyl spectrum i.e. Quasi-Similarity and the dominant condition will be used.

Characterisation of weyl spectrum in Hilbert spaces

In this paper, the study give some continuity properties of the Weyl spectrum of a continuous linear operator on a Banach space and show that the Weyl’s theorem holds for a spectral operator of finite type although the theorem fails for a spectral operator in general.

Totally (m, n)-paranormal operators

In this paper, we investigate the class of totally (m, n)-paranormal operators on Hilbert space and prove some additional properties of totally (m, n)-paranormal operators on Hilbert space. Also, we show that Weyl's theorem holds for operators in this class. Moreover, we also show that for totally (m, n)-paranormal operators, the Weyl spectrum satisfies the spectral mapping theorem.

A Note on the Order Lozanovsky Spectrum for Positive Operators

In this note we consider the order Lozanovsky spectrum of a positive operator on a complex Banach lattice and show that it generally contains the order Weyl spectrum, settling a weaker form of a question raised in Alekhno (Positivity 13(1):3–20, 2009).

Perturbations of Weyl’s Theorems for Unbounded Class-A Operators

The significance of Weyl's spectrum is regional to the perturbation theory but recently it is related to operator theory in some theorems. The study of Weyl’s theorem has so far limited to the class of bounded operators, however, lately this study has been extended to some classes of unbounded operators such as hypanormal, posinormal and class- operators. The aim of this article is to continue study more spectral properties for class- operators. First, we use property to study property (b) and then show the equivalent of property (gb) with property (gw). Secondly, we start to study new spectral properties that was defined for bounded operators we start with and properties and show that for any operator that belongs to class- will possess them. Finally, we resuming our goal and give our last two properties and and prove them for , also we established the connection between these properties.

Stability of relative essential spectra involving relative demicompactness concept in Banach subalgebra

This paper develops the notion of relative demicompact elements of an algebra with respect to a Banach subalgebra as a generalization of relative demicompact linear operators acting on Banach spaces. Drawing on this novel notion, we build a new class of Fredholm perturbation regarding a given Banach subalgebra B which contains its inessential ideal kB and the set of left Fredholm perturbations suggested in [6]. The developed class of Fredholm perturbation exhibits that is a two-sided closed ideal of B that is key in the characterization of the weyl spectrum of elements affiliated with B.

Demicompactness perturbation in Banach algebras and some stability results

Abstract In this paper, we introduce and investigate a new concept that we call demicompact elements in Banach algebras as a generalization of demicompact linear operators acting on Banach spaces. Our concept is used to construct a new class of Fredholm perturbations with respect to a given Banach subalgebra B, that contains an inessential ideal k B {k_{B}} and the set of left Fredholm perturbations introduced in [A. Ben Ali and N. Moalla, Fredholm perturbation theory and some essential spectra in Banach algebra with respect to subalgebra, Indag. Math. (N. S.) 28 2017, 2, 276–286]. We show that it is a two-sided closed ideal of B playing an important role in the characterization of the Weyl spectrum of elements affiliated with B.

Phase of quantum oscillation in Weyl semimetals

We consider the semiclassical quantization condition for the energy of an electron in a magnetic field in the case when the electron orbit lies on a Fermi-surface pocket surrounding the Weyl point of a topological semimetal and analyze the constant γ appearing in this condition. It is shown that this constant has the universal value, γ = 0, independent on the tilt of the Weyl spectrum. Since the constant γ for an extremal cross section of the Fermi surface determines the phase of quantum oscillations, this result explains why measurements of the phase permit one to find Weyl points in crystals even though the extremal cross section of the pocket does not pass through this point, and the appropriate Berry phase of the orbit differs from π.

Self-adjoint perturbations of left (right)Weyl spectrum for upper triangular operator matrices

Let H be a separable infinite-dimensional Hilbert space. Given the operators A ? B(H) and B ? B(H), we define MX := [A X 0 B] where X ? S(H) is a self-adjoint operator. In this paper, a necessary and sufficient condition is given for MX to be a left (right) Weyl operator for some X ? S(H). Moreover, it is shown that ? X?S(H) ?*(MX) = ? X?S(H)?Inv(H) ?*(MX) = ? X?B(H) ?*(MX) ? ?, where ?* is the left (right)Weyl spectrum. Finally, we further characterize the perturbation of the left (right) Weyl spectrum for Hamiltonian operators.

Continuity of spectra on class of p-wA(s,t) operators

In this paper, we show that spectrum, Weyl spectrum and Browder spectrum are continuous on the set of p-wA(s,t) operators with 0 < p ? 1 and 0 < s, t, s + t ? 1.

A new variant of Hildebrandt’s theorem for the Weyl spectrum in Banach spaces

The main purpose of this paper is to establish a new variant of the Hildebrandt?s theorem for the Weyl spectrum in a separable Banach space. This theorem asserts that the convex hull of the Weyl spectrum of an operator T is equal to the intersection of the Weyl numerical spectra of operators that are similar to T.

Universal spin wave damping in magnetic Weyl semimetals

We analyze the decay of spin waves into Stoner excitations in magnetic Weyl semimetals. The lifetime of a mode is found to have a universal dependence on its frequency and momentum, and on a few parameters that characterize the relativistic Weyl spectrum. At the same time, Gilbert damping by Weyl electrons is absent. The decay rate of spin waves is calculated perturbatively using the s-d model of itinerant Weyl or Dirac electrons coupled to local moments. We show that many details of the Weyl spectrum, such as the momentum-space locations, dispersions and sizes of the Weyl Fermi pockets, can be deduced indirectly by probing the spin waves of local moments using inelastic neutron scattering.

Continuity of the spectrum and Weyl type theorems for extension of 2-isometric operators

In this paper, we show that the spectrum, Weyl spectrum, and Browder spectrum are continuous on the set of all 2-quasi-2-isometric operators. Further, we show that k-quasi-2-isometric operator satisfies Bishop's property β. Moreover, we prove Weyl type theorems for f(dTS), where dTS denote the generalized derivation or the elementary operator with k-quasi-2-isometric operator entries T and S* and f ∈ H(σ(dTS)), the set of analytic functions which are defined on an open neighborhood of σ(dTS).

Large Fermi-Energy Shift and Suppression of Trivial Surface States in NbP Weyl Semimetal Thin Films.

Weyl semimetals, a class of 3D topological materials, exhibit a unique electronic structure featuring linear band crossings and disjoint surface states (Fermi-arcs). While first demonstrations of topologically driven phenomena have been realized in bulk crystals, efficient routes to control the electronic structure have remained largely unexplored. Here, a dramatic modification of the electronic structure in epitaxially grown NbP Weyl semimetal thin films is reported, using in situ surface engineering and chemical doping strategies that do not alter the NbP lattice structure and symmetry, retaining its topological nature. Through the preparation of a dangling-bond-free, P-terminated surface which manifests in a surface reconstruction, all the well-known trivial surface states of NbP are fully suppressed, resulting in a purely topological Fermi-arc dispersion. In addition, a substantial Fermi-energy shift from -0.2to 0.3 eVacross the Weyl points is achieved bysurfacechemical doping, unlocking access to the hitherto unexplored n-type region of the Weyl spectrum. These findings constitute a milestone toward surface-state and Fermi-level engineering of topological bands in Weyl semimetals, and, whilethere are still challenges in minimizing doping-driven disorder and grain boundary density in the films,they do represent a major advance to realize device heterostructures based on Weyl physics.

Anomalous Josephson effect and quantum anomaly in inversion asymmetric Weyl semimetals

We study a Josephson junction involving an inversion-asymmetric Weyl semimetal in presence of time-reversal symmetric (TRS) or time-reversal symmetry broken tilt in the Weyl spectra. We reveal that both types of tilts in the Weyl nodes lead to a Josephson $0$-$\pi$ transition and a zero bias valley/chiral supercurrent. Strikingly, the TRS tilt gives rise to a pure valley Josephson current (VJC) and TRS broken tilt induces a pure chirality Josephson current (CJC) in this system. The VJC and CJC are the manifestation of valley symmetry broken and $\mathbb{Z}_2$ symmetry broken by the respective tilt. We obtain the reversal of a pure VJC and pure CJC even in the zero bias condition controllable by the junction length. Our analysis of controllability of valley and chirality dependent transport in an inversion asymmetric Weyl semimetal junction could allow applications in valleytronics and chiralitytronics, respectively. The tilt induced Josephson effect provides an alternative route for supercurrent $0$-$\pi$ transition, different from the conventional ferromagnetism Josephson junctions where the spin polarization is essential. In the long junction and zero temperature limit, VJC and CJC are associated with a quantum anomaly which is manifested through a discontinuous jump in the current in absence of TRS and TRS breaking tilts, respectively.

New approach to a-Weyl’s theorem and some preservation results

In this paper, we introduce and study new spectral properties called (bz) and $$(w_{\pi _{00}^{a}})$$ in connection with a-Weyl type theorems, which are analogous respectively to a-Weyl’s theorem and a-Browder’s theorem. Among other results, we prove that a bounded linear operator T satisfies property (bz) if and only if T satisfies a-Browder’s theorem and $$\sigma _{uf}(T)=\sigma _{uw}(T),$$ where $$\sigma _{uf}(T)$$ and $$\sigma _{uw}(T)$$ are respectively, the upper semi-Fredholm spectrum and the upper Weyl spectrum. Furthermore, the property (bz) is characterized for an operator T through localized SVEP, and its preservation under direct sum of two bounded linear operators is also examined. The theory is exemplified in the case of some special classes of operators. We also prove the following new result that’s $$\sigma _{uf}(T)=\sigma _{uw}(T)\Longleftrightarrow \sigma _{ubf}(T)=\sigma _{ubw}(T),$$ for every bounded linear operator T.

Weyl Spectrum of Upper Triangular Operator Matrices

This paper is concerned with general n × n upper-triangular operator matrices with given diagonal entries. The characterizations of perturbations of their left (resp. right) Weyl spectrum and Weyl spectrum are given, based on the space decomposition technique. Moreover, some sufficient and necessary conditions are given under which the left (resp. right) Weyl spectrum and the Weyl spectrum of such operator matrix, respectively, coincide with the union of the left (resp. right) Weyl spectrum and the Weyl spectrum of its diagonal entries.

On the spectral mapping theorem for Weyl spectra of Toeplitz operators

In this paper we study the approximate point spectrum and the surjectivity spectrum of a Toeplitz operators $$T_\phi$$ , defined on Hardy spaces $$H^2(\mathbf{T })$$ of the unit circle $$\mathbf{T }$$ of $${\mathbb {C}}$$ , where the symbol $$\phi \in L^\infty (\mathbf{T })$$ , or $$\phi$$ is a continuous symbol. We also extend some results obtained by Farenick and Lee (Trans Am Math Soc 348(10):4153–4174, 1996). In particular, we study Weyl type theorems and the spectral mapping theorem for the Weyl spectra.