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991.
Kaufman?s theorem (Kaufman, 1978 [9]) on representing closed linear operators as quotients of bounded operators is given a new constructive proof, and is extended to operators between two Hilbert spaces. Two different definitions of operator quotients existing in the literature are compared. 相似文献
992.
We introduce the monotone Sokolov property and show that it is dual to monotone retractability in the sense that X is monotonically retractable if and only if Cp(X) is monotonically Sokolov. Besides, a space X is monotonically Sokolov if and only if Cp(X) is monotonically retractable. Monotone retractability and monotone Sokolov property are shown to be preserved by R-quotient images and Fσ-subspaces. Furthermore, every monotonically retractable space is Sokolov so it is collectionwise normal and has countable extent. We also establish that if X and Cp(X) are Lindelöf Σ-spaces then they are both monotonically retractable and have the monotone Sokolov property. An example is given of a space X such that Cp(X) has the Lindelöf Σ-property but neither X nor Cp(X) is monotonically retractable. We also establish that every Lindelöf Σ-space with a unique non-isolated point is monotonically retractable. On the other hand, each Lindelöf space with a unique non-isolated point is monotonically Sokolov. 相似文献
993.
994.
Gajath Gunatillake Mirjana Jovovic Wayne Smith 《Journal of Mathematical Analysis and Applications》2014
The operator that takes the function f to ψf°φ is a weighted composition operator. We study numerical ranges of some classes of weighted composition operators on H2, the Hardy–Hilbert space of the unit disc. We consider the case where φ is a rotation of the unit disc and identify a class of convexoid operators. In the case of isometric weighted composition operators we give a complete classification of their numerical ranges. We also consider the inclusion of zero in the interior of the numerical range. 相似文献
995.
We give a probabilistic construction of frequently hypercyclic or universal entire functions using Birkhoff?s ergodic Theorem. We apply the same ideas to construct random frequently universal vectors for the polynomials of the weighted backward shift on the classical real or complex ?p space. 相似文献
996.
In this paper we identify certain classes of non-stretch mappings that enjoy a sharp estimate of the Beurling–Ahlfors operator. We first make use of a property of subharmonic functions to prove that the Bañuelos–Wang conjecture and the Iwaniec conjecture are true for a class of mappings that satisfy a quasilinear conjugate Beltrami equation. By utilizing the principal solutions of Beltrami equations, we further explicitly construct some classes of non-stretch mappings for which the Bañuelos–Wang conjecture and the Iwaniec conjecture are true. 相似文献
997.
In this paper, the singular second order differential operators are considered defined on the multi-interval. Some boundary and transmission conditions are imposed on the maximal domain functions with the spectral parameter. After constructing the differential operators associated with the boundary value transmission problems on the suitable Hilbert spaces, it is proved that these operators are the maximal dissipative operators. Finally constructing the model operators which are established with the help of the scattering functions, it is proved that all root vectors of the maximal dissipative operators are complete in the Hilbert spaces. 相似文献
998.
This paper aims to study the preservation of log-concavity for Bernstein-type operators. In particular, attention is focused on positive linear operators, defined on the positive semi-axis, admitting a probabilistic representation in terms of a process with independent increments. This class includes the classical Gamma, Szász, and Szász–Durrmeyer operators. With respect to the first and second operators, the results of this paper correct two erroneous counterexamples in [10]. As a main tool in our results we use stochastic order techniques. Our results include, as a particular case, the log-concavity of certain functions related to the incomplete Gamma function. 相似文献
999.
We establish a Harnack inequality for finite connected graphs with non-negative Ricci curvature. As a consequence, we derive an eigenvalue lower bound, extending previous results for Ricci flat graphs. 相似文献
1000.
We give conditions on the kernel function (or activation function) for the family of radial basis function (RBF) neural networks obtained upon replacing the usual translation by the Delsarte one, with not necessarily the same smoothing factor in all kernel nodes, to have the universal approximation property in suitable weighted Lp-spaces (1?p<∞). A complete characterization of such kernels for p=1 and p=2 is provided. 相似文献