Gantmacher-Krein Theorem for 2-totally Nonnegative Operators in Ideal Spaces

2010 ◽  
pp. 395-410 ◽  
Author(s):  
Olga Y. Kushel ◽  
Petr P. Zabreiko
Keyword(s):  
Krein Theorem

The Adamyan-Arov-Krein theorem: Vectorial variant

1987 ◽  
Vol 37 (5) ◽  
pp. 1297-1306
Author(s):  
S. R. Treil'
Keyword(s):  
Krein Theorem

The nevanlinna-adamyan-arov-krein theorem in the semidefinite case

1995 ◽  
Vol 76 (4) ◽  
pp. 2542-2549 ◽  
Author(s):  
A. Ya. Kheifetz
Keyword(s):  
Krein Theorem

The Krasnosel'skii-Krein Theorem for Differential Inclusions

2005 ◽  
Vol 41 (7) ◽  
pp. 1049-1053 ◽  
Author(s):  
N. V. Plotnikova
Keyword(s):  
Differential Inclusions ◽  
Krein Theorem

scholarly journals Gantmacher-Kreĭn theorem for 2 nonnegative operators in spaces of functions

2006 ◽  
Vol 2006 ◽  
pp. 1-15 ◽  
Author(s):  
O. Y. Kushel ◽  
P. P. Zabreiko
Keyword(s):  
Completely Continuous ◽  
Nonnegative Operator ◽  
The Difference ◽  
Krein Theorem ◽  
Exterior Square

The existence of the second (according to the module) eigenvalueλ2of a completely continuous nonnegative operatorAis proved under the conditions thatAacts in the spaceLp(Ω)orC(Ω)and its exterior squareA∧Ais also nonnegative. For the case when the operatorsAandA∧Aare indecomposable, the simplicity of the first and second eigenvalues is proved, and the interrelation between the indices of imprimitivity ofAandA∧Ais examined. For the case whenAandA∧Aare primitive, the difference (according to the module) ofλ1andλ2from each other and from other eigenvalues is proved.

Nonlinear eigenvalue–eigenvector problems for STP matrices

2002 ◽  
Vol 132 (6) ◽  
pp. 1307-1331
Author(s):  
Uri Elias ◽  
Allan Pinkus
Keyword(s):  
Totally Positive ◽  
Krein Theorem ◽  
Image Position ◽  
Nonlinear Eigenvalue

Let Ai, i = 1, …, m, be a set of Ni × Ni−1 strictly totally positive (STP) matrices, with N0 = Nm = N. For a vector x = (x1, …, xN) ∈ RN and arbitrary p > 0, set We consider the eigenvalue-eigenvector problem where p1 … pm−1 = r. We prove an analogue of the classical Gantmacher-Krein theorem for the eigenvalue-eigenvector structure of STP matrices in the case where pi ≥ 1 for each i, plus various extensions thereof.

Vector variant of the Adamyan—Arov—Krein theorem

1986 ◽  
Vol 20 (1) ◽  
pp. 74-76 ◽  
Author(s):  
S. R. Treil’
Keyword(s):  
Krein Theorem ◽  
Vector Variant
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