# Representations of compact linear operators in Banach spaces and nonlinear eigenvalue problems

## Related Articles

- Absolutely summing linear operators into spaces with no finite cotype. Botelho, Geraldo; Pellegrino, Daniel // Bulletin of the Belgian Mathematical Society - Simon Stevin;May2009, Vol. 16 Issue 2, p373
Given an infinite-dimensional Banach space X and a Banach space Y with no finite cotype, we determine whether or not every continuous linear operator from X to Y is absolutely (q; p)-summing for various choices of p and q, including the case p = q. If X assumes its cotype, the problem is solved...

- A Fredholm alternative-like result on power bounded operators. Ülger, Ali; Yavuz, Onur // Turkish Journal of Mathematics;2011, Vol. 35 Issue 3, p473
Let X be a complex Banach space and T : X â†’ X be a power bounded operator, i.e., supnâ‰¥0 ||Tn|| < âˆž. We write B(X) for the Banach algebra of all bounded linear operators on X. We prove that the space Ran (I - T) is closed if and only if there exist a projection Î¸ âˆˆ B(X)...

- Convergence Results for a Common Solution of a Finite Family of Equilibrium Problems and Quasi-Bregman Nonexpansive Mappings in Banach Space. Ugwunnadi, G. C.; Ali, Bashir // Journal of Operators;3/24/2016, p1
We introduce an iterative process for finding common fixed point of finite family of quasi-Bregman nonexpansive mappings which is a unique solution of some equilibrium problem.

- On K-groups of operator algebras on HD spaces and QD spaces. Li Qiong Lin; Huai Jie Zhong; Yun Nan Zhang // Acta Mathematica Sinica;Dec2010, Vol. 26 Issue 12, p2355
We obtain the K-groups of the operator ideals contained in the class of Riesz operators. And based on the results, we calculate the K-groups of the operator algebras on HD spaces and QD spaces.

- POWERS OF OPERATORS DOMINATED BY STRICTLY SINGULAR OPERATORS. FLORES, JULIO; HERN�NDEZ, FRANCISCO L.; TRADACETE, PEDRO // Quarterly Journal of Mathematics;Sep2008, Vol. 59 Issue 3, p321
It is proved that every positive operator R on a Banach lattice E dominated by a strictly singular operator T:E ? E satisfies that the R4 is strictly singular. Moreover, if E is order continuous then the R2 is already strictly singular.

- Families of positive operators with reverse order. Pestil, Şebnem Yildiz // Studia Universitatis Babes-Bolyai, Mathematica;Jun2012, Vol. 57 Issue 2, p295
The objective of this paper is to present several invariant subspace results for collections of positive operators on Banach lattices. For any family C of positive operators in L(E), I will reverse order.

- More on (É‘,Î²)-Normal Operators in Hilbert Spaces. Eskandari, Rasoul; Mirzapour, Farzollah; Morassaei, Ali // Abstract & Applied Analysis;2012, p1
We study some properties of (Î±,Î²)-normal operators and we present various inequalities between the operator norm and the numerical radius of (Î±,Î²)-normal operators on Banach algebra B(H) of all bounded linear operators T : H --Â» H, where H is Hilbert space.

- An extension of a theorem of E. A. Barbashin to the dichotomy of abstract evolution operators. Preda, Ciprian; Preda, Petre // Bulletin of the Belgian Mathematical Society - Simon Stevin;Nov2010, Vol. 17 Issue 4, p705
Anecessary and sufficient condition for the uniformexponential dichotomy is pointed out using a discrete-time argument. Thus are extended known results due to Barbashin [1], Datko [7], Lovelady [10], Pazy[13], Preda[14, 15, 16].

- Pseudospectra of semigroup generators. Shargorodsky, E. // Bulletin of the London Mathematical Society;Dec2010, Vol. 42 Issue 6, p1031
It is proved that the resolvent norm of the infinitesimal generator of a C0 semigroup on a complex uniformly convex Banach space cannot be constant on a nonempty open set. In the case of Hilbert spaces, this result answers a question posed by J. R. Partington.