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Semi-Browder operators and perturbations

Vladimir Rakočević (1997)

Studia Mathematica

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].

Single valued extension property and generalized Weyl’s theorem

M. Berkani, N. Castro, S. V. Djordjević (2006)

Mathematica Bohemica

Let T be an operator acting on a Banach space X , let σ ( T ) and σ B W ( T ) be respectively the spectrum and the B-Weyl spectrum of T . We say that T satisfies the generalized Weyl’s theorem if σ B W ( T ) = σ ( T ) ∖ E ( T ) , where E ( T ) is the set of all isolated eigenvalues of T . The first goal of this paper is to show that if T is an operator of topological uniform descent and 0 is an accumulation point of the point spectrum of T , then T does not have the single valued extension property at 0 , extending an earlier result of J. K. Finch and a...

Solvability conditions for elliptic problems with non-Fredholm operators

V. Volpert, B. Kaźmierczak, M. Massot, Z. Peradzyński (2002)

Applicationes Mathematicae

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...

Some examples concerning applicability of the Fredholm-Radon method in potential theory

Josef Král, Wolfgang L. Wendland (1986)

Aplikace matematiky

Simple examples of bounded domains D ⊂ 𝐑 3 are considered for which the presence of peculiar corners and edges in the boundary δ D causes that the double layer potential operator acting on the space 𝒮 ( δ D ) of all continuous functions on δ D can for no value of the parameter α be approximated (in the sub-norm) by means of operators of the form α I + T (where I is the identity operator and T is a compact linear operator) with a deviation less then | α | ; on the other hand, such approximability turns out to be possible for...

Some generic properties of nonlinear second order diffusional type problem

Vladimír Ďurikovič, Mária Ďurikovičová (1999)

Archivum Mathematicum

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.

Spectra originating from semi-B-Fredholm theory and commuting perturbations

Qingping Zeng, Qiaofen Jiang, Huaijie Zhong (2013)

Studia Mathematica

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 σ d s c ( T + F ) = σ d s c ( T ) 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...

Spectral approximation for Segal-Bargmann space Toeplitz operators

Albrecht Böttcher, Hartmut Wolf (1997)

Banach Center Publications

Let A stand for a Toeplitz operator with a continuous symbol on the Bergman space of the polydisk N or on the Segal-Bargmann space over ℂ N . 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 A n of A to the linear span of the monomials z 1 k 1 . . . z N k N : 0 ≤ k j ≤ n . Unfortunately, in general the spectrum of A n does not mimic the spectrum of A as...

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