SVEP and compact perturbations

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 ...

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 ).

Bishop's property, SVEP and Dunford Property

ON COMPACT PERTURBATIONS AND COMPACT RESOLVENTS OF NONLINEAR m-ACCRETIVE OPERATORS IN BANACH SPACES

Several mapping results are given involving compact perturbations and compact resolvents of accretive and m-accretive operators. A simple and straightforward proof is given to an important special case of a result of Morales who has recently improved and/or extended various results by the author and Hirano. Improved versions of results of Browder and Morales are shown to be possible by studying...

Mapping Theorems Involving Compact Perturbations and Compact Resolvents of Nonlinear Operators in Banach Spaces

where it is assumed that the “resolvent” L, = (T + (l/n)l)-i, II = 1, 2,... exists and is defined at least on the range of the operator f C. Such a class of operators T includes all m-accretive operators (cf. Kato ] 5 I). The equations (G,) can be solved by a degree theory argument if we assume, among other things, that L, is compact and C is continuous and bounded, or that L, is continuous and...