On common fixed points of pairs of a single and a multivalued coincidentally commuting mappings in -metric spaces.
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.
Let I ⊂ ℝ be an interval, Y be a normed linear space and Z be a Banach space. We investigate the Banach space Lip₂(I,Z) of all functions ψ: I → Z such that , where [r,s,t;ψ]:= ((s-r)ψ(t)+(t-s)ψ(r)-(t-r)ψ(s))/((t-r)(t-s)(s-r)). We show that ψ ∈ Lip₂(I,Z) if and only if ψ is differentiable and its derivative ψ’ is Lipschitzian. Suppose the composition operator N generated by h: I × Y → Z, (Nφ)(t):= h(t,φ(t)), maps the set (I,Y) of all affine functions φ: I → Y into Lip₂(I,Z). We prove that if N is...
One-term and multi-term fractional differential equations with a basic derivative of order α ∈ (0,1) are solved. The existence and uniqueness of the solution is proved by using the fixed point theorem and the equivalent norms designed for a given value of parameters and function space. The explicit form of the solution obeying the set of initial conditions is given.