Spectral decomposability of rank-one perturbations of normal operators

Rank one perturbations of self-adjoint operators

On Decomposability of Compact Perturbations of Operators

Let A be a Hilbert-space operator satisfying the growth condition ||(z —/4) || < expi&[dist(z, /)]~SS, z //.where / is a C Jordan curve, and K > 0, s £ (0, 1) are two constants. Let T = A + B for some fi e C , I < p < oc. It is shown that T is strongly decomposable if and only if cr(T') does not fill the "interior" of /. 1, H. Radjavi and the author [13] showed that if a Hilbert-space operator ...

Spectral Analysis of Rank One Perturbations and Applications

A review or Lhe general lheory of ~df-lVljoillt operatoro or lhe form A + on where n is nlll].;: one is presellled, Applicl1liu,,~ ine!llde proofs of loealizatiun fur S'chr(idingcr operators. resl111s un illVClse Spt'ct.n11 t.\'J()ory, and examples of opcn1lorH wilh singular cOljt.inl1ou~ ~peclruj)).

Point Spectrum and Mixed Spectral Types for Rank One Perturbations

We consider examples Aλ = A + λ(φ, · )φ of rank one perturbations with φ a cyclic vector for A. We prove that for any bounded measurable set B ⊂ I, an interval, there exists A,φ so that {E ∈ I | some Aλ has E as an eigenvalue} agrees with B up to sets of Lebesgue measure zero. We also show that there exist examples where Aλ has a.c. spectrum [0,1] for all λ, and for sets of λ’s of positive Lebe...

some properties of fuzzy hilbert spaces and norm of operators

in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...