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An operator in a Banach space is called upper (resp. lower) semi-Browder if it is upper (lower) semi-Fredholm and has a finite ascent (resp. descent). An operator in a Banach space is called semi-Browder if it is upper semi-Browder or lower semi-Browder. We prove the stability of the semi-Browder operators under commuting Riesz operator perturbations. As a corollary we get some results of Grabiner [6], Kaashoek and Lay [8], Lay [11], Rakočević [15] and Schechter [16].
Let be an operator acting on a Banach space , let and be respectively the spectrum and the B-Weyl spectrum of . We say that satisfies the generalized Weyl’s theorem if , where is the set of all isolated eigenvalues of . The first goal of this paper is to show that if is an operator of topological uniform descent and is an accumulation point of the point spectrum of then does not have the single valued extension property at , extending an earlier result of J. K. Finch and a...
The paper is devoted to solvability conditions for linear elliptic problems with non-Fredholm operators. We show that the operator becomes normally solvable with a finite-dimensional kernel on properly chosen subspaces. In the particular case of a scalar equation we obtain necessary and sufficient solvability conditions. These results are used to apply the implicit function theorem for a nonlinear elliptic problem; we demonstrate the persistence of travelling wave solutions to spatially periodic...
Simple examples of bounded domains are considered for which the presence of peculiar corners and edges in the boundary causes that the double layer potential operator acting on the space of all continuous functions on can for no value of the parameter be approximated (in the sub-norm) by means of operators of the form (where is the identity operator and is a compact linear operator) with a deviation less then ; on the other hand, such approximability turns out to be possible for...
We are interested of the Newton type mixed problem for the general second order semilinear evolution equation. Applying Nikolskij’s decomposition theorem and general Fredholm operator theory results, the present paper yields sufficient conditions for generic properties, surjectivity and bifurcation sets of the given problem.
Burgos, Kaidi, Mbekhta and Oudghiri [J. Operator Theory 56 (2006)] provided an affirmative answer to a question of Kaashoek and Lay and proved that an operator F is of power finite rank if and only if for every operator T commuting with F. Later, several authors extended this result to the essential descent spectrum, left Drazin spectrum and left essential Drazin spectrum. In this paper, using the theory of operators with eventual topological uniform descent and the technique used by Burgos et...
Let A stand for a Toeplitz operator with a continuous symbol on the Bergman space of the polydisk or on the Segal-Bargmann space over . Even in the case N = 1, the spectrum Λ(A) of A is available only in a few very special situations. One approach to gaining information about this spectrum is based on replacing A by a large “finite section”, that is, by the compression of A to the linear span of the monomials . Unfortunately, in general the spectrum of does not mimic the spectrum of A as...
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