Search results for "Weyl"
showing 10 items of 69 documents
Simplified feedback control system for scanning tunneling microscopy
2021
A Scanning Tunneling Microscope (STM) is one of the most important scanning probe tools available to study and manipulate matter at the nanoscale. In a STM, a tip is scanned on top of a surface with a separation of a few \AA. Often, the tunneling current between tip and sample is maintained constant by modifying the distance between the tip apex and the surface through a feedback mechanism acting on a piezoelectric transducer. This produces very detailed images of the electronic properties of the surface. The feedback mechanism is nearly always made using a digital processing circuit separate from the user computer. Here we discuss another approach, using a computer and data acquisition thr…
On Hurwitz spaces of coverings with one special fiber
2009
Let X X' Y be a covering of smooth, projective complex curves such that p is a degree 2 etale covering and f is a degree d covering, with monodromy group Sd, branched in n + 1 points one of which is a special point whose local monodromy has cycle type given by the partition e = (e1,...,er) of d. We study such coverings whose monodromy group is either W(Bd) or wN(W(Bd))(G1)w-1 for some w in W(Bd), where W(Bd) is the Weyl group of type Bd, G1 is the subgroup of W(Bd) generated by reflections with respect to the long roots ei - ej and N(W(Bd))(G1) is the normalizer of G1. We prove that in both cases the corresponding Hurwitz spaces are not connected and hence are not irreducible. In fact, we s…
Hurwitz spaces of coverings with two special fibers and monodromy group a Weyl group of typeBd
2012
f! Y; where is a degree-two coverings with n1 branch points and branch locus D and f is a degree-d coverings with n2 points of simple branching and two special points whose local monodromy is given by e and q, respectively. Furthermore the covering f has monodromy group Sd and f. D /\ D fD? where D f denotes the branch locus of f . We prove that the corresponding Hurwitz spaces are irreducible under the hypothesis n2 s r dC 1.
A Unifying Approach to Weyl Type Theorems for Banach Space Operators
2013
Weyl type theorems have been proved for a considerably large number of classes of operators. In this paper, by introducing the class of quasi totally hereditarily normaloid operators, we obtain a theoretical and general framework from which Weyl type theorems may be promptly established for many of these classes of operators. This framework also entails Weyl type theorems for perturbations f(T + K), where K is algebraic and commutes with T, and f is an analytic function, defined on an open neighborhood of the spectrum of T + K, such that f is non constant on each of the components of its domain.
On generalized a-Browder's theorem
2007
We characterize the bounded linear operators T satisfying generalized a-Browder's theorem, or generalized a-Weyl's theorem, by means of localized SVEP, as well as by means of the quasi-nilpotent part H0(�I T) asbelongs to certain sets of C. In the last part we give a general framework in which generalized a-Weyl's theorem follows for several classes of operators. 1. Preliminaries. Let L(X) denote the space of bounded linear oper- ators on an infinite-dimensional complex Banach space X. For T ∈ L(X), denote by α(T) the dimension of the kernel ker T, and by β(T) the codi- mension of the range T(X). The operator T ∈ L(X) is called upper semi- Fredholm if α(T) < ∞ and T(X) is closed, and lower …
Property (R) under perturbations
2012
Property (R) holds for a bounded linear operator $${T \in L(X)}$$ , defined on a complex infinite dimensional Banach space X, if the isolated points of the spectrum of T which are eigenvalues of finite multiplicity are exactly those points λ of the approximate point spectrum for which λI − T is upper semi-Browder. In this paper we consider the permanence of this property under quasi nilpotent, Riesz, or algebraic perturbations commuting with T.
Property (w) and perturbations
2007
A bounded linear operator T ∈ L(X) defined on a Banach space X satisfies property (w), a variant of Weyl’s theorem, if the complement in the approximate point spectrum σa(T ) of the Weyl essential approximate spectrum σwa(T ) coincides with the set of all isolated points of the spectrum which are eigenvalues of finite multiplicity. In this note, we study the stability of property (w), for a bounded operator T acting on a Banach space, under perturbations by finite rank operators, by nilpotent operator and quasi-nilpotent operators commuting with T .
Weyl type theorems for bounded linear operators on Banach spaces
2011
In 1909 H. Weyl [59] studied the spectra of all compact linear perturbations of a self-adjoint operator defined on a Hilbert space and found that their intersection consisted precisely of those points of the spectrum where are not isolated eigenvalues of nite multiplicity. Later, the property established by Weyl for self-adjoint operators has been observed for several other classes of operators, for instance hyponormal operators on Hilbert spaces, Toeplitz operators,convolution operators on group algebras, and many other classes of operators ned on Banach spaces . In the literature, a bounded linear operator defined on a Banach space which satisfies this property is said to satisfy Weyl's t…
Some characterizations of operators satisfying a-Browder's theorem
2005
Abstract We characterize the bounded linear operators T defined on Banach spaces satisfying a-Browder's theorem, or a-Weyl's theorem, by means of the discontinuity of some maps defined on certain subsets of C . Several other characterizations are given in terms of localized SVEP, as well as by means of the quasi-nilpotent part, the hyper-kernel or the analytic core of λ I − T .
Creating stable Floquet–Weyl semimetals by laser-driving of 3D Dirac materials
2017
Nature Communications 8, 13940 (2017). doi:10.1038/ncomms13940