there are many different ways to subdivide the spectrum of a bounded linear operator; some of them aremotivated by applications to physics (in particular, quantum mechanics). in this study, the relationship betweenthe subdivisions of spectrum which are not required to be disjoint and goldberg's classification are given.moreover, these subdivisions for some summability methods are studied.

We study the Hankel determinant of the generalized Jacobi weight (x − t)x(1 − x) for x ∈ [0, 1] with α, β > 0, t < 0 and γ ∈ R. Based on the ladder operators for the corresponding monic orthogonal polynomials Pn(x), it is shown that the logarithmic derivative of Hankel determinant is characterized by a τ -function for the Painlevé VI system.

Let T and C be two Hilbert space operators. We prove that if T is near, in a certain sense, to an operator completely polynomially dominated with a finite bound by C, then T is similar to an operator which is completely polynomially dominated by the direct sum of C and a suitable weighted unilateral shift. Among the applications, a refined Banach space version of Rota similarity theorem is give...

In this paper we completely characterize compact Toeplitz operators on the harmonic Bergman space. By using this result we establish the short exact sequences associated with the Toeplitz algebra and the Hankel algebra. We show that the Fredholm index of each Fredholm operator in the Toeplitz algebra or the Hankel algebra is zero.  2002 Elsevier Science (USA). All rights reserved.

We show that a big Hankel operator on the standard Hardy space of the polydisk D, n > 1, cannot be compact unless it is the zero operator. We also show that this result can be generalized to certain Hankel operators defined on Hardy-Sobolev spaces of the polydisk.

A class of matrices is studied that could be considered as Hankel matrices with respect to a system of orthogonal polynomials. It is shown that they have similar properties like classical Hankel matrices. Main attention is paid to the construction of fast and superfast algorithms. The main tool is the fact that these matrices are matrix representation of multiplication operators.

Nuclearity of the Hankel operator is a known sufficient condition for convergence of Lyapunov-balanced truncations. We show how a previous result on nuclearity of Hankel operators of systems with an analytic semigroup can be extended to systems with a semigroup of class D with p ≥ 1 (the case p = 1 being the analytic case). For semigroups that are generated by a Dunford-Schwartz spectral operat...

Connections between Hankel transforms of different order for L-functions are examined. Well known are the results of Guy [Guy] and Schindler [Sch]. Further relations result from projection formulae for Bessel functions of different order. Consequences for Hankel multipliers are exhibited and implications for radial Fourier multipliers on Euclidean spaces of different dimensions indicated.