scholarly journals The almost Dunford–Pettis property of semi-compact operators

2012 ◽  
Vol 45 (1) ◽  
Author(s):  
Belmesnaoui Aqzzouz ◽  
Aziz Elbour
Keyword(s):  
Compact Operator ◽  
Sufficient Conditions ◽  
Compact Operators ◽  
Necessary And Sufficient Conditions ◽  
Necessary And Sufficient

AbstractWe establish necessary and sufficient conditions for which each positive semi-compact operator (resp. the second power of a positive semi-compact operator) is almost Dunford–Pettis (resp. Dunford–Pettis).

scholarly journals Compact Operators for Almost Conservative and Strongly Conservative Matrices

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
S. A. Mohiuddine ◽  
M. Mursaleen ◽  
A. Alotaibi
Keyword(s):  
Compact Operator ◽  
Hausdorff Measure ◽  
Measure Of Noncompactness ◽  
Sufficient Conditions ◽  
Compact Operators ◽  
Necessary And Sufficient Conditions ◽  
Hausdorff Measure Of Noncompactness ◽  
Matrix Classes ◽  
Necessary And Sufficient ◽  
Conservative Matrix

We obtain the necessary and sufficient conditions for an almost conservative matrix to define a compact operator. We also establish some necessary and sufficient (or only sufficient) conditions for operators to be compact for matrix classes(f,X), whereX=c,c0,l∞. These results are achieved by applying the Hausdorff measure of noncompactness.

scholarly journals COMPACT DIFFERENCES OF COMPOSITION OPERATORS ON BERGMAN SPACES IN THE BALL

2010 ◽  
Vol 89 (3) ◽  
pp. 407-418 ◽  
Author(s):  
XIANG DONG YANG ◽  
LE HAI KHOI
Keyword(s):  
Unit Ball ◽  
Composition Operator ◽  
Composition Operators ◽  
Bergman Spaces ◽  
Sufficient Conditions ◽  
Compact Operators ◽  
Necessary And Sufficient Conditions ◽  
Weighted Bergman Spaces ◽  
Finite Sum ◽  
Necessary And Sufficient

AbstractWe obtain necessary and sufficient conditions for the compactness of differences of composition operators acting on the weighted Bergman spaces in the unit ball. A representation of a composition operator as a finite sum of composition operators modulo compact operators is also studied.

Interpolation problems for ideals in nest algebras

1992 ◽  
Vol 111 (1) ◽  
pp. 151-160 ◽  
Author(s):  
M. Anoussis ◽  
E. G. Katsoulis ◽  
R. L. Moore ◽  
T. T. Trent
Keyword(s):  
Hilbert Space ◽  
Interpolation Problem ◽  
Bounded Operator ◽  
Sufficient Conditions ◽  
Compact Operators ◽  
Necessary And Sufficient Conditions ◽  
Nest Algebras ◽  
Interpolation Problems ◽  
The One ◽  
Necessary And Sufficient

AbstractGiven vectors x and y in a Hilbert space, an interpolating operator is a bounded operator T such that Tx = y. An interpolating operator for n vectors satisfies the equation Txt = yt, for i = 1, 2,, n. In this article, we continue the investigation of the one-vector interpolation problem for nest algebras that was begun by Lance. In particular, we require the interpolating operator to belong to certain ideals which have proved to be of importance in the study of nest algebras, namely, the compact operators, the radical, Larson's ideal, and certain other ideals. We obtain necessary and sufficient conditions for interpolation in each of these cases.

scholarly journals Compact operators on some generalized mixed norm spaces

Filomat ◽  
2014 ◽  
Vol 28 (5) ◽  
pp. 1019-1026
Author(s):  
A. Alotaibi ◽  
E. Malkowsky ◽  
H. Nergiz
Keyword(s):  
Hausdorff Measure ◽  
Measure Of Noncompactness ◽  
Sufficient Conditions ◽  
Compact Operators ◽  
Necessary And Sufficient Conditions ◽  
Mixed Norm ◽  
Hausdorff Measure Of Noncompactness ◽  
Mixed Norm Spaces ◽  
Necessary And Sufficient

We establish identities or estimates for the Hausdorff measure of noncompactness of operators from some generalized mixed norm spaces into any of the spaces c0, c, ?1, and [?1, ??]<m(?)>. Furthermore we give necessary and sufficient conditions for the operators in these cases to be compact. Our results are complementary to those in [1, 3, 13].

The extinction time of a general birth and death process with catastrophes

1986 ◽  
Vol 23 (04) ◽  
pp. 851-858 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Laplace Transform ◽  
Size Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Death Process ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Different Types ◽  
The Laplace Transform ◽  
Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj&gt; 0 for eachj&gt; 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

Nonlinear boundary-value problems for degenerate differential-algebraic systems

2020 ◽  
Vol 17 (3) ◽  
pp. 313-324
Author(s):  
Sergii Chuiko ◽  
Ol'ga Nesmelova
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Algebraic System ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Weakly Nonlinear ◽  
Differential Algebraic System ◽  
Linear Differential ◽  
Necessary And Sufficient

The study of the differential-algebraic boundary value problems, traditional for the Kiev school of nonlinear oscillations, founded by academicians M.M. Krylov, M.M. Bogolyubov, Yu.A. Mitropolsky and A.M. Samoilenko. It was founded in the 19th century in the works of G. Kirchhoff and K. Weierstrass and developed in the 20th century by M.M. Luzin, F.R. Gantmacher, A.M. Tikhonov, A. Rutkas, Yu.D. Shlapac, S.L. Campbell, L.R. Petzold, Yu.E. Boyarintsev, V.F. Chistyakov, A.M. Samoilenko, O.A. Boichuk, V.P. Yacovets, C.W. Gear and others. In the works of S.L. Campbell, L.R. Petzold, Yu.E. Boyarintsev, V.F. Chistyakov, A.M. Samoilenko and V.P. Yakovets were obtained sufficient conditions for the reducibility of the linear differential-algebraic system to the central canonical form and the structure of the general solution of the degenerate linear system was obtained. Assuming that the conditions for the reducibility of the linear differential-algebraic system to the central canonical form were satisfied, O.A.~Boichuk obtained the necessary and sufficient conditions for the solvability of the linear Noetherian differential-algebraic boundary value problem and constructed a generalized Green operator of this problem. Based on this, later O.A. Boichuk and O.O. Pokutnyi obtained the necessary and sufficient conditions for the solvability of the weakly nonlinear differential algebraic boundary value problem, the linear part of which is a Noetherian differential algebraic boundary value problem. Thus, out of the scope of the research, the cases of dependence of the desired solution on an arbitrary continuous function were left, which are typical for the linear differential-algebraic system. Our article is devoted to the study of just such a case. The article uses the original necessary and sufficient conditions for the solvability of the linear Noetherian differential-algebraic boundary value problem and the construction of the generalized Green operator of this problem, constructed by S.M. Chuiko. Based on this, necessary and sufficient conditions for the solvability of the weakly nonlinear differential-algebraic boundary value problem were obtained. A typical feature of the obtained necessary and sufficient conditions for the solvability of the linear and weakly nonlinear differential-algebraic boundary-value problem is its dependence on the means of fixing of the arbitrary continuous function. An improved classification and a convergent iterative scheme for finding approximations to the solutions of weakly nonlinear differential algebraic boundary value problems was constructed in the article.

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