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Approximation properties determined by operator ideals and approximability of homogeneous polynomials and holomorphic functions

Sonia Berrios, Geraldo Botelho (2012)

Studia Mathematica

Given an operator ideal ℐ, a Banach space E has the ℐ-approximation property if the identity operator on E can be uniformly approximated on compact subsets of E by operators belonging to ℐ. In this paper the ℐ-approximation property is studied in projective tensor products, spaces of linear functionals, spaces of linear operators/homogeneous polynomials, spaces of holomorphic functions and their preduals.

Approximation results for nonlinear integral operators in modular spaces and applications

Ilaria Mantellini, Gianluca Vinti (2003)

Annales Polonici Mathematici

We obtain modular convergence theorems in modular spaces for nets of operators of the form ( T w f ) ( s ) = ∫ H K w ( s - h w ( t ) , f ( h w ( t ) ) ) d μ H ( t ) , w > 0, s ∈ G, where G and H are topological groups and h w w > 0 is a family of homeomorphisms h w : H → h w ( H ) ⊂ G . Such operators contain, in particular, a nonlinear version of the generalized sampling operators, which have many applications in the theory of signal processing.

Approximation theorems for compactifications

Kotaro Mine (2011)

Colloquium Mathematicae

We shall show several approximation theorems for the Hausdorff compactifications of metrizable spaces or locally compact Hausdorff spaces. It is shown that every compactification of the Euclidean n-space ℝⁿ is the supremum of some compactifications homeomorphic to a subspace of ℝ n + 1 . Moreover, the following are equivalent for any connected locally compact Hausdorff space X: (i) X has no two-point compactifications, (ii) every compactification of X is the supremum of some compactifications whose remainder...

Arbitrage and pricing in a general model with flows

Jan Palczewski (2003)

Applicationes Mathematicae

We study a fundamental issue in the theory of modeling of financial markets. We consider a model where any investment opportunity is described by its cash flows. We allow for a finite number of transactions in a finite time horizon. Each transaction is held at a random moment. This places our model closer to the real world situation than discrete-time or continuous-time models. Moreover, our model creates a general framework to consider markets with different types of imperfection: proportional...

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