Fuzzy best simultaneous approximation of a finite number of functions is considered. For this purpose, a fuzzy norm on $Cleft (X, Y right )$ and its fuzzy dual space and also the  set of subgradients of a fuzzy norm are introduced. Necessary case of a proved theorem about characterization of simultaneous approximation will be extended to the fuzzy case.

The calculation of RTS amounts to measuring a relationship between inputs and outputs in a production structure. There are many methods to measure RTS in the primal space or the dual space. One of the main approaches is using the multiplier on the convexity constraint. But returns to scale measurements in DEA models are affected by the presence of regulatory constraints. These additional constr...

Let X be a NLS. Consider the set of all bounded linear functionals on X, and associate the norm defined above (as an exercise verify that it is indeed a norm). The resulting space, denoted X∗, is called the dual of X. It is another exercise to verify that X∗ is a Banach space (even if X isn’t). We can also consider the double dual X∗∗. It is easy to show that X is naturally imbedded in X∗∗ by t...

In a recent paper [4] we obtained explicit examples of twistor spaces that are associated to a compact self-dual four-manifold admitting a Killing field, and also determined their moduli space. In this note we investigate minitwistor spaces associated to these twistor spaces. We determine their structures, minitwistor lines and also their moduli space. In particular, we show that the moduli spa...

We introduce and study the family of Besov–Köthe spaces which is a generalization of the Besov spaces, the Besov–Morrey spaces and the variable Besov spaces. As an application of the general results for the Besov–Köthe spaces, we identify a pre-dual of the Besov–Morrey space.

We consider C-algebras generated by a single Hilbert bimodule (Pimsner-Toeplitz algebras) and by a product systems of Hilbert bimodules. We give a new proof of a theorem of Pimsner, which states that any representation of the generating bimodule gives rise to a representation of the Pimsner-Toeplitz algebra. Our proof does not make use of the conditional expectation onto the subalgebra invarian...

In [5] we showed, that a doubly transitive, non-solvable dimensional dual hyperoval D is either isomorphic to the Mathieu dual hyperoval or to a quotient of a Huybrechts dual hyperoval. In order to determine the doubly transitive dimensional dual hyperovals, it remains to classify the doubly transitive, solvable dimensional dual hyperovals and this paper is a contribution to this problem. A dou...

Let (M, ∂M) be a compact 3-manifold with boundary which admits a complete, convex co-compact hyperbolic metric. We are interested in the following question: Question A Let h be a (non-smooth) metric on ∂M , with curvature K > −1. Is there a unique hyperbolic metric g on M , with convex boundary, such that the induced metric on ∂M is h ? There is also a dual statement: Question B Let h be a (non...

For a Hilbert space H of functions let H H be the space of weak products of functions in H, i.e. all functions h that can be written as h = ∑∞ i=1 figi for some fi, gi ∈ H with ∑∞ i=1 ‖fi‖‖gi‖ <∞. Let D denote the Dirichlet space of the unit circle ∂D, i.e. the nontangential limits of functions f ∈ Hol(D) with ∫ D |f ′|2dA < ∞ and let Dh be the harmonic Dirichlet space, which consists of functi...

The cohomology of operator algebras introduced by B. E. Johnson, R. V. Kadison, and J. R. Ringrose in a series of three papers is a useful tool for obtaining new invariants for operator algebras or to prove stability results by the vanishing of their cohomology groups (see [14]). If X is a von Neumann algebra and a Banach bimodule over M, and if « is a positive integer, then the nth cohomology ...