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Non-self mappings in modular spaces and common fixed point theorems

Abdolrahman Razani, Valdimir Rakočević, Zahraa Goodarzi (2010)

Open Mathematics

The aim of this paper, is to introduce the convex structure (specially, Takahashi convex structure) on modular spaces. Moreover, we are interested in proving some common fixed point theorems for non-self mappings in modular space.

Non-trivial derivations on commutative regular algebras.

A. F. Ber, Vladimir I. Chilin, Fyodor A. Sukochev (2006)

Extracta Mathematicae

Necessary and sufficient conditions are given for a (complete) commutative algebra that is regular in the sense of von Neumann to have a non-zero derivation. In particular, it is shown that there exist non-zero derivations on the algebra L(M) of all measurable operators affiliated with a commutative von Neumann algebra M, whose Boolean algebra of projections is not atomic. Such derivations are not continuous with respect to measure convergence. In the classical setting of the algebra S[0,1] of all...

(Non-)weakly mixing operators and hypercyclicity sets

Frédéric Bayart, Étienne Matheron (2009)

Annales de l’institut Fourier

We study the frequency of hypercyclicity of hypercyclic, non–weakly mixing linear operators. In particular, we show that on the space 1 ( ) , any sublinear frequency can be realized by a non–weakly mixing operator. A weaker but similar result is obtained for c 0 ( ) or p ( ) , 1 < p < . Part of our results is related to some Sidon-type lacunarity properties for sequences of natural numbers.

Nonzero and positive solutions of a superlinear elliptic system

Mario Zuluaga Uribe (2001)

Archivum Mathematicum

In this paper we consider the existence of nonzero solutions of an undecoupling elliptic system with zero Dirichlet condition. We use Leray-Schauder Degree Theory and arguments of Measure Theory. We will show the existence of positive solutions and we give applications to biharmonic equations and the scalar case.

Norm attaining and numerical radius attaining operators.

María D. Acosta, Rafael Payá (1989)

Revista Matemática de la Universidad Complutense de Madrid

In this note we discuss some results on numerical radius attaining operators paralleling earlier results on norm attaining operators. For arbitrary Banach spaces X and Y, the set of (bounded, linear) operators from X to Y whose adjoints attain their norms is norm-dense in the space of all operators. This theorem, due to W. Zizler, improves an earlier result by J. Lindenstrauss on the denseness of operators whose second adjoints attain their norms, and is also related to a recent result by C. Stegall...

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