ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

8. Analysis

1991 MS Classification: 41, 46, 47 Tiţa, Nicolae, Transilvania University Braşov, Romania Bilinear operators and some generalizations of the approximation spaces Let (x, ∥ · ∥) a normed Abelian group and ∥ · ∥^{∗} an other norm on X. We consider the sequence (En(f)), where (En(f)) = inf{∥f − g∥ : ∥g∥^{∗} < n}. Φ will a norming function and φ : [0, ∞) → [0, ∞) is a continuous function such that φ(0) = 0, φ(x + y) ≤ φ(x) + φ(y) and φ is increasing. The generalized approximation spaces X_{Φ}^{φ} are defined as follows:

X_{Φ}^{φ} = {f ∈ X : Φ ({φ (En(f))}) < φ}

For φ(t) = t^{p} , 0 < p ≤ 1 we obtain the spaces X_{Φ}^{p}. If B : X × X → X is a biliniar and bounded operator s. t. ∥B(f, g)∥^{∗} < n^{2} if ∥f∥ < n , ∥g∥ < n, then B : Xφ ; Φ̄ × Xφ ; Φ̄ → Xφ ; Φ̄ is also founded if

Φ̄ : (En(f)) → Φ (\frac{En(f)}{n}) .