In this contribution, we discuss some unique common fixed point theorems for three and four occasionally weakly compatible mappings satisfying different types of contractive condition.
Some strong convergence theorems of common fixed points of asymptotically nonexpansive mappings in the intermediate sense are obtained. The results presented in this paper improve and extend the corresponding results in Huang, Khan and Takahashi, Chang, Schu, and Rhoades.
It is proved that for a von Neumann algebra A ⊆ B(ℋ ) the subspace of normal maps is dense in the space of all completely bounded A-bimodule homomorphisms of B(ℋ ) in the point norm topology if and only if the same holds for the corresponding unit balls, which is the case if and only if A is atomic with no central summands of type . Then a duality result for normal operator modules is presented and applied to the following problem. Given an operator space X and a von Neumann algebra A, is the map...
Let , 0 ≤ t ≤ 1, be Banach spaces obtained via complex interpolation. With suitable hypotheses, linear operators T that act boundedly on both and will act boundedly on each . Let denote such an operator when considered on , and denote its spectrum. We are motivated by the question of whether or not the map is continuous on (0,1); this question remains open. In this paper, we study continuity of two related maps: (polynomially convex hull) and (boundary of the polynomially convex...
Let G be a locally compact Polish group with an invariant metric. We provide sufficient and necessary conditions for the existence of a compact set A ⊆ G and a sequence such that for all n. It is noticed that such measures μ form a meager subset of all probabilities on G in the weak measure topology. If for some k the convolution power has nontrivial absolutely continuous component then a similar characterization is obtained for any locally compact, σ-compact, unimodular, Hausdorff topological...
In the paper the fundamental properties of discrete dynamical systems generated by an -condensing mapping ( is the Kuratowski measure of noncompactness) are studied. The results extend and deepen those obtained by M. A. Krasnosel’skij and A. V. Lusnikov in [21]. They are also applied to study a mathematical model for spreading of an infectious disease investigated by P. Takac in [35], [36].
2000 Mathematics Subject Classification: 47A65, 45S78.Connection of characteristic functions S(z) of nonunitary operator T with the functions of Caratheodori class is established. It was demonstrated that the representing measures from integral representation of the function of Caratheodori's class are defined by restrictions of spectral measures of unitary dilation, of a restricted operator T on the corresponding defect subspaces.