Some more weak Hubert spaces
We construct, by a variation of the method used to construct the Tsirelson spaces, a new family of weak Hilbert spaces which contain copies of l₂ inside every subspace.
Some natural families of M-ideals.
Some new results on accretive multivalued operators
Some notes about the convexity module.
Some permanence results of properties of Banach spaces
Using some known lifting theorems we present three-space property type and permanence results; some of them seem to be new, whereas other are improvements of known facts.
Some properties of -convexity.
Some properties of Pythagorean modulus.
Some properties of weakly countably determined Banach spaces
Some properties on the closed subsets in Banach spaces
It is shown that under natural assumptions, there exists a linear functional does not have supremum on a closed bounded subset. That is the James Theorem for non-convex bodies. Also, a non-linear version of the Bishop-Phelps Theorem and a geometrical version of the formula of the subdifferential of the sum of two functions are obtained.
Some Ramsey type theorems for normed and quasinormed spaces
We prove that every bounded, uniformly separated sequence in a normed space contains a “uniformly independent” subsequence (see definition); the constants involved do not depend on the sequence or the space. The finite version of this result is true for all quasinormed spaces. We give a counterexample to the infinite version in for each 0 < p < 1. Some consequences for nonstandard topological vector spaces are derived.
Some recent results concerning weak Asplund spaces
Some remarks on generalised lush spaces
D. Tan, X. Huang and R. Liu [Studia Math. 219 (2013)] recently introduced the notion of generalised lush (GL) spaces, which, at least for separable spaces, is a generalisation of the concept of lushness introduced by Boyko et al. [Math. Proc. Cambridge Philos. Soc. 142 (2007)]. The main result of D. Tan et al. is that every GL-space has the so called Mazur-Ulam property (MUP). In this note, we prove some further properties of GL-spaces, for example, every M-ideal in a...
Some remarks on inequalities that characterize inner product spaces.
Some remarks on sub-differential calculus.
Mean value inequalities are shown for functions which are sub- or super-differentiable at every point.
Some remarks on symmetric basic sequences in L1
Some remarks on the duality mapping
Some remarks on the equality
We show that the equality is a necessary condition for the validity of certain results about isomorphic properties in the projective tensor product of two Banach spaces under some approximation property type assumptions.
Some Remarks On The Fixed Point Stability For Nonexpansive Mappings
Some remarks on the uniform approximation property in Banach spaces
Some remarks on ultrapowers and superproperties of the sum and interpolation spaces of Banach spaces