No abstract

We give an example of a Banach lattice with a non-convex modulus of monotonicity, which disproves a claim made in the literature. Results on preservation of the non-strict Opial property and Opial property under passing to general direct sums of Banach spaces are established.

We study interpolation spaces obtained via a general discrete interpolation method based on a Banach space with an unconditional basis. We find conditions which guarantee that such interpolation spaces have the Opial property and the uniform Opial property.

An estimate for the modulus of convexity and characteristic of convexity of a general direct sum of Banach spaces is established. Using direct sums, we construct a space with given characteristic of convexity and the value of the modulus of convexity at [Formula: see text]. A result on uniform convexity of spaces obtained with the general discrete interpolation method is proved.