Property (gab) through localized SVEP

Bishop's property, SVEP and Dunford Property

Bishop’s Property (β), Svep and Dunford Property (c) ∗

If S, T ∈ B(H) have Bishop's property (β), does S + T have Bishop's property (β)? In this paper, a special case of this question is studied. Also given are a necessary and sufficient condition for a 2 × 2 operator matrix to have Bishop's property (β). Finally, the Helton class of an operator which has Bishop's property (β) is studied. 1. Introduction. Let B(H) be the algebra of all bounded line...

Consistent in invertibility operators and SVEP

If S(X ) ⊂ B(X ), where B(X ) denotes the algebra of operators on a Banach space X , then A ∈ B(X ) is S(X ) consistent if AB ∈ S(X ) ⇐⇒ BA ∈ S(X ) for every B ∈ B(X ). SVEP is a powerful tool in determining the S(X ) consistency of operators A for various choices of the subset S(X ).

Upper Triangular Operator Matrices , SVEP and Browder , Weyl Theorems

A Banach space operator T ∈ B(X ) is polaroid if points λ ∈ isoσσ(T ) are poles of the resolvent of T . Let σa(T ), σw(T ), σaw(T ), σSF+(T ) and σSF−(T ) denote, respectively, the approximate point, the Weyl, the Weyl essential approximate, the upper semi–Fredholm and lower semi–Fredholm spectrum of T . For A, B and C ∈ B(X ), let MC denote the operator matrix (

Localized biomolecular sensing enabled through plasmonic nanocavities

We propose and study an integrated refractive index sensor which is based on a plasmonic slot cavity integrated on silicon-on-insulator wafers. In this device, the guided mode is vertically coupled to the cavity which is a metal-dielectricmetal waveguide and is separated from a photonic wire waveguide by a silicon dioxide spacer. We perform an in-depth study that links the geometrical parameter...