On where has infinitely many “bumps”
On decomposably regular operators.
On determination of eigenvalues and eigenvectors of selfadjoint operators
Two simple methods for approximate determination of eigenvalues and eigenvectors of linear self-adjoint operators are considered in the following two cases: (i) lower-upper bound of the spectrum of is an isolated point of ; (ii) (not necessarily an isolated point of with finite multiplicity) is an eigenvalue of .
On Dominant Operators.
On Dominating Sequences in the Unit Disc.
On extended eigenvalues and extended eigenvectors of truncated shift
In this paper we consider the truncated shift operator Su on the model space K2u := H2 θ uH2. We say that a complex number λ is an extended eigenvalue of Su if there exists a nonzero operator X, called extended eigenvector associated to λ, and satisfying the equation SuX = λXSu. We give a complete description of the set of extended eigenvectors of Su, in the case of u is a Blaschke product..
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 generalized topological divisors of zero
On Intertwining Operators.
On J. C. Alexander's theorem
On joint spectra
On joint spectra of commuting families of operators
On joint spectra of operators on a Banach space isomorphic to its square
On Lattice Isomorphisms with Positive Real Spectrum and Groups of Positive Operators.
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 local spectral properties of operators in Banach spaces
On local spectral radius
On (n,k)-quasiparanormal operators
Let T be a bounded linear operator on a complex Hilbert space . For positive integers n and k, an operator T is called (n,k)-quasiparanormal if for x ∈ . The class of (n,k)-quasiparanormal operators contains the classes of n-paranormal and k-quasiparanormal operators. We consider some properties of (n,k)-quasiparanormal operators: (1) inclusion relations and examples; (2) a matrix representation and SVEP (single valued extension property); (3) ascent and Bishop’s property (β); (4) quasinilpotent...
On nonnegative operators and fully cyclic peripheral spectrum.