Kushel, O. Y.; Zabreiko, P. P.
January 2006
Abstract & Applied Analysis;2006, p1
Academic Journal
The existence of the second (according to the module) eigenvalue λ2 of a completely continuous nonnegative operator A is proved under the conditions that A acts in the space Lp(Ω) or C(Ω) and its exterior square A?A is also nonnegative. For the case when the operators A and A ∧ A are indecomposable, the simplicity of the first and second eigenvalues is proved, and the interrelation between the indices of imprimitivity of A and A ∧ A is examined. For the case when A and A ∧ A are primitive, the difference (according to the module) of λ1 and λ2 from each other and from other eigenvalues is proved.


Related Articles

  • (σ,Ï„)-Higher derivations. Hejazian, Shirin; Mahdavian Rad, Hussein; Mirzavaziri, Madjid // Journal of Advanced Research in Pure Mathematics;2012, Vol. 4 Issue 4, p67 

    Let σ, τ be linear mappings on an algebra A. A sequence {dn}n=0∞ of linear mappings on A is said to be a (σ, τ )-higher derivation if ..., for each a, b ∈ A and each nonnegative integer n. We are going to characterize (σ, τ )- higher derivations in terms of (σ,...

  • Inverse spectral problems of the theory of identification of linear dynamic systems. Valeev, N. F.; Yumagulov, M. G. // Automation & Remote Control;Nov2009, Vol. 70 Issue 11, p1776 

    The problem of restoration of the parameters of the linear operator from a finite set of eigenvalues was considered. A new scheme of its solution was proposed, both the necessary and sufficient conditions for existence of solutions were presented, and a procedure of their numerical construction...

  • COMMUTATIONAL PROPERTIES OF POWERS OF OPERATORS OF MIXED TYPE INCREASING THE POWERS. Hristova, Miryana S. // Dialogue (1311-9206);Sep2013, Issue 3, p54 

    The operators ... were considered in [11] with non-negative integers, p q ∈ ⇔+. Here they are considered with parameters p < q +1 in the space S of the polynomials with complex coefficients or in the space A0 of functions analytic in neighbourhoods of the origin. Power series...

  • CMV Matrices and Little and Big −1 Jacobi Polynomials. Derevyagin, Maxim; Vinet, Luc; Zhedanov, Alexei // Constructive Approximation;Dec2012, Vol. 36 Issue 3, p513 

    We introduce a new map from polynomials orthogonal on the unit circle to polynomials orthogonal on the real axis. This map is closely related to the theory of CMV matrices. It contains an arbitrary parameter λ which leads to a linear operator pencil. We show that the little and big −1...

  • Some results on generalized σ-derivations. Amin, Hosseini; Mahmoud, Hassani; Asadollah, Niknam // Journal of Advanced Research in Pure Mathematics;2013, Vol. 5 Issue 3, p61 

    Let A and B be two Banach algebras and let M be a Banach B-bimodule. Suppose that σ : A → B is a linear mapping and δ : A → M is a (σ,d)-derivation. Two results about automatic continuity of (σ, d)-derivations is proved. In this article it is proved that eδσ,...

  • LINEAR PRESERVERS OF G-ROW AND G-COLUMN MAJORIZATION ON Mn,m. ARMANDNEJAD, A.; MOHAMMADI, Z.; AKBARZADEH, F. // Bulletin of the Iranian Mathematical Society;2013, Vol. 39 Issue 5, p865 

    Let A and B be n × m matrices. The matrix B is said to be g-row majorized (respectively g-column majorized) by A, denoted by B

  • Weighted composition operators of H8 into a-Bloch spaces on the unit ball. Min Zhang; Huai Chen // Acta Mathematica Sinica;Feb2009, Vol. 25 Issue 2, p265 

    In this paper we characterize the boundedness and compactness of weighted composition operators of H8 into a-Bloch spaces on the unit ball in C n.

  • Boundedness for Multilinear Commutator of Bochner-Riesz Operator with Weighted Lipschitz Functions. Huang Mingliang; Liu Lanzhe // International Journal of Open Problems in Computer Science & Mat;Sep2011, Vol. 4 Issue 3, p116 

    In this paper, we obtain the boundedness for the multilinear commutators related to the Bochner-Riesz operator with weighted Lipschitz functions.

  • On Some Applications of the Ordinary and Extended Duhamel Products. Karaev, M. // Siberian Mathematical Journal;May2005, Vol. 46 Issue 3, p431 

    LetC(D) denote the algebra of alln-times continuously differentiable functions onholomorphic on the unit diskD= {z?C: |z|<1}. We prove thatC(D) is a Banach algebra with multiplication the Duhamel productand describe its maximal ideal space. Using the Duhamel product we prove that the extended...


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics