Interpolation of Ideal Measures by Abstract K and J Spaces

Interpolation of the measure of non-compactness of bilinear operators among quasi-Banach spaces

“…We refer to the books by Peetre [40] and Brudnyǐ and Krugljak [6] and the paper by Nilsson [38] for the basic theory on the general real interpolation method. Other properties of this method can be found, for example, in the papers by Cwikel and Peetre [17], Nilsson [39], Cobos, Fernández-Cabrera, Manzano and Martínez [9], Fernández-Cabrera and Martínez [26] or Cobos, Fernández-Cabrera and Martínez [10].…”

Interpolation of a measure of weak non-compactness

“…We also note that interpolation properties of a different type were established by Aksoy and Maligranda [2], Cobos, Manzano and Martínez [11], and Cobos and Martínez [12,13] for the real method and Fernández-Cabrera and Martínez [17] for the abstract real method.…”

Mean separations in Banach spaces under abstract interpolation and extrapolation

“…Quantitative studies were undertaken for a measure of noncompactness [9] and for the measures related to closed operator ideals [14]. The aim of a quantitative treatment is to obtain estimates for certain measures of deviation from a given property, which may provide also qualitative results.…”