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We work with interpolation methods for $N$-tuples of Banach spaces associated with polygons. We compare necessary conditions for interpolating closed operator ideals with conditions required to interpolate compactness. We also establish a formula for the measure of non-compactness of interpolated operators.
Two new species of gastropods belonging to the volutid genus Adelomelon Dall, 1906 are described from Tertiary strata of Patagonia, Argentina. Adelomelon posei n. sp. was found in the lower part of the Gran Bajo del Gualicho Formation (Río Negro Province), which is currently dated as Late Eocene through Middle Miocene in age. Adelomelon valdesiense n. sp. comes from the Puerto Madryn Formation (Chubut Province) of early Late Miocene age. Both species are characterized by angulated biconical teleodonch whorls and strongly developed rows of axial nodes, similar in shape to those of some Recent species of Adelomelon, but positioned differently. Discovery of two new species of the genus Adelomelon in the Tertiary of Patagonia significantly extends the known stratigraphic range of this genus from Late Eocene(?)—Miocene to Recent.
We show that certain interpolation results for compact operators established by Cobos and co-workers cannot be extended to general closed operator ideals. We shall also characterize compactness of an embedding in terms of functions related to the classical K- and J-functionals of interpolation theory.
The paper establishes estimates for ideal measures of operators interpolated by the real method in terms
of the measures of their restrictions to a sequence of spaces modelled on the intersection. It also shows that
the estimates are optimal.
We establish an estimate for the measure of non-compactness of an interpolated operator acting from a J-space into a K-space. Our result refers to general Banach N-tuples. We also derive estimates for entropy numbers if some of the N-tuples reduce to a single Banach space.
We study the relationship between the dual of the K-space defined by means of a polygon and the J-space generated by the dual N-tuple. The results complete the research started in . Special attention is paid to the case when the N-tuple is formed by Banach lattices
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