On decomposably regular operators.
On generalized a-Browder's theorem
We characterize the bounded linear operators T satisfying generalized a-Browder's theorem, or generalized a-Weyl's theorem, by means of localized SVEP, as well as by means of the quasi-nilpotent part H₀(λI - T) as λ belongs to certain sets of ℂ. In the last part we give a general framework in which generalized a-Weyl's theorem follows for several classes of operators.
On generalized property (v) for bounded linear operators
An operator T acting on a Banach space X has property (gw) if , where is the approximate point spectrum of T, is the upper semi-B-Weyl spectrum of T and E(T) is the set of all isolated eigenvalues of T. We introduce and study two new spectral properties (v) and (gv) in connection with Weyl type theorems. Among other results, we show that T satisfies (gv) if and only if T satisfies (gw) and .
On inessential and improjective operators.
We give several characterizations of the improjective operators, introduced by Tarafdar, and we characterize the inessential operators among the improjective operators. It is an interesting problem whether both classes of operators coincide in general. A positive answer would provide, for example, an intrinsic characterization of the inessential operators. We give several equivalent formulations of this problem and we show that the inessential operators acting between certain pairs of Banach spaces...
On Kato non-singularity
An exactness lemma offers a simplified account of the spectral properties of the "holomorphic" analogue of normal solvability.
On limits of -norms of an integral operator
A recurrence relation for the computation of the -norms of an Hermitian Fredholm integral operator is derived and an expression giving approximately the number of eigenvalues which in absolute value are equal to the spectral radius is determined. Using the -norms for the approximation of the spectral radius of this operator an a priori and an a posteriori bound for the error are obtained. Some properties of the a posteriori bound are discussed.
On one subset M. Schechter's essential spectrum
On operators T such that Weyl's theorem holds for f(T).
On regularities and Fredholm theory
We investigate the relationship between the regularities and the Fredholm theory in a Banach algebra.
On Riesz and Inessential Operators.
On semi-Fredholm operators and the conjugate of a product of operators
On some local spectral theory and bounded local resolvent of operator matrices
We extend and generalize some results in local spectral theory for upper triangular operator matrices to upper triangular operator matrices with unbounded entries. Furthermore, we investigate the boundedness of the local resolvent function for operator matrices.
On the approximation numbers of large Toeplitz matrices.
On the axiomatic theory of spectrum
There are a number of spectra studied in the literature which do not fit into the axiomatic theory of Żelazko. This paper is an attempt to give an axiomatic theory for these spectra, which, apart from the usual types of spectra, like one-sided, approximate point or essential spectra, include also the local spectra, the Browder spectrum and various versions of the Apostol spectrum (studied under various names, e.g. regular, semiregular or essentially semiregular).
On the axiomatic theory of spectrum II
We give a survey of results concerning various classes of bounded linear operators in a Banach space defined by means of kernels and ranges. We show that many of these classes define a spectrum that satisfies the spectral mapping property.
On the computation of some quantities in the theory of Fredholm operators
On the essential approximate point spectrum II
On the essential spectra of matrix operators and applications.
On the existence of solution of the equation and a generalized coincidence degree theory. II.
On the generalized boundary value problem
In the paper it is proved that the generalized linear boundary value problem generates a Fredholm operator. Its index depends on the number of boundary conditions. The existence results of Landesman-Lazer type are given as an application to nonlinear problems by using dual generalized boundary value problems.