-convexity and duality for almost summing operators.
In this paper we establish Kannan-type cyclic contraction results in probabilistic 2-metric spaces. We use two different types of -norm in our theorems. In our first theorem we use a Hadzic-type -norm. We use the minimum -norm in our second theorem. We prove our second theorem by different arguments than the first theorem. A control function is used in our second theorem. These results generalize some existing results in probabilistic 2-metric spaces. Our results are illustrated with an example....
A new sufficient condition for the asymptotic stability of a locally Lipschitzian Markov semigroup acting on the space of signed measures is proved. This criterion is applied to the semigroup of Markov operators generated by a Poisson driven stochastic differential equation.
T. Kato [5] found an important property of semi-Fredholm pencils, now called the Kato decomposition. M. A. Kaashoek [3] introduced operators having the property P(S:k) as a generalization of semi-Fredholm operators. In this work, we study this class of operators. We show that it is characterized by a Kato-type decomposition. Other properties are also proved.
In analogy to the classical isomorphism between ((ℝⁿ), and (resp. and ), we show that a large class of moderate linear mappings acting between the space of compactly supported generalized functions and (ℝⁿ) of generalized functions (resp. the space of Colombeau rapidly decreasing generalized functions and the space of temperate ones) admits generalized integral representations, with kernels belonging to specific regular subspaces of (resp. ). The main novelty is to use accelerated...
A Coburn theorem says that a nonzero Toeplitz operator on the Hardy space is one-to-one or its adjoint operator is one-to-one. We study the corresponding problem for certain Toeplitz operators on the Bergman space.
We investigate the structure of the set of solutions of the Cauchy problem x’ = f(t,x), x(0) = x₀ in Banach spaces. If f satisfies a compactness condition expressed in terms of measures of weak noncompactness, and f is Pettis-integrable, then the set of pseudo-solutions of this problem is a continuum in , the space of all continuous functions from I to E endowed with the weak topology. Under some additional assumptions these solutions are, in fact, weak solutions or strong Carathéodory solutions,...