THE ISOMETRIC EXTENSION OF AN INTO MAPPING FROM THE UNIT SPHERE S[e(Γ)] TO THE UNIT SPHERE S(E)

This is such a article to consider an ＂into＂ isometric mapping between two unit spheres of two infinite dimensional spaces of different types. In this article, we find a useful condition （using the Krein-Milman property） under which an into-isometric mapping from the unit sphere of e（Γ） to the unit sphere of a normed space E can be linearly isometric extended.

The Properties of k-quasi-＊-A（n） Operator

An operator T is called k-quasi-*-A(n) operator, if T^(*k)|T^(1+n)|^(2/(1+n))T^k ≥T^(*k)|T~* |~2T^k , k ∈ Z, which is a generalization of quasi-*-A(n) operator. In this paper we prove some properties of k-quasi-*-A(n) operator, such as, if T is a k-quasi-*-A(n) operator and N(T )■N(T~* ), then its point spectrum and joint point spectrum are identical. Using these results, we also prove that if T is a k-quasi-*-A(n) operator and N(T )■N(T ), then the spectral mapping theorem holds for the Weyl spectrum and for the essential approximate point spectrum.

Property(ω)and the Single-valued Extension Property

By the new spectrum originated from the single-valued extension property,we give the necessary and sufficient conditions for a bounded linear operator defined on a Banach space for which property(ω)holds.Meanwhile,the relationship between hypercyclic property(or supercyclic property)and property(ω)is discussed.

Property(ω_1) and Single Valued Extension Property

In this note we study the property（ω1）,a variant of Weyl＇s theorem by means of the single valued extension property,and establish for a bounded linear operator defined on a Banach space the necessary and sufficient condition for which property（ω1） holds.As a consequence of the main result,the stability of property（ω1） is discussed.

Components of generalized Kato resolvent set and single-valued extension property

In this paper, we use the constancy of certain subspace valued mappings on the components of the generalized Kato resolvent set and the equivalences of the single-valued extension property at a point 0 for operators which admit a generalized Kato decomposition to obtain a classification of the components of the generalized Kato resolvent set of operators. We also give some applications of these results

LOCAL SPECTRA OF UNILATERAL OPERATOR WEIGHTED SHIFTS

In this note, the local spectral properties of unilateral operator weighted shifts are studied.

A Note on the Browder's and Weyl's Theorem

Let T be a Banach space operator, E（T） be the set of all isolated eigenvalues of T and π（T） be the set of all poles of T. In this work, we show that Browder＇s theorem for T is equivalent to the localized single-valued extension property at all complex numbers λ in the complement of the Weyl spectrum of T, and we give some characterization of Weyl＇s theorem for operator satisfying E（T） = π（T）. An application is also given.

Insights into channel potentials and electron quasi-Fermi potentials for DG tunnel FETs

A detailed investigation carried out, with the help of extensive simulations using the TCAD device simulator Sentaurus, with the aim of achieving an understanding of the effects of variations in gate and drain potentials on the device characteristics of a silicon double-gate tunnel field effect transistor（Si-DG TFET） is reported in this paper. The investigation is mainly aimed at studying electrical properties such as the electric potential, the electron density, and the electron quasi-Fermi potential in a channel. From the simulation results, it is found that the electrical properties in the channel region of the DG TFET are different from those for a DG MOSFET. It is observed that the central channel potential of the DG TFET is not pinned to a fixed potential even after the threshold is passed（as in the case of the DG MOSFET）; instead, it initially increases and later on decreases with increasing gate voltage, and this is also the behavior exhibited by the surface potential of the device. However, the drain current always increases with the applied gate voltage. It is also observed that the electron quasi-Fermi potential（e QFP）decreases as the channel potential starts to decrease, and there are hiphops in the channel e QFP for higher applied drain voltages. The channel regime resistance is also observed for higher gate length, which has a great effect on the I–V characteristics of the DG TFET device. These channel regime electrical properties will be very useful for determining the tunneling current; thus these results may have further uses in developing analytical current models.