Some open problems on best approximation in normed linear spaces
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 problems arising in connection with the theory of vector measures
Some problems on narrow operators on function spaces
It is known that if a rearrangement invariant (r.i.) space E on [0, 1] has an unconditional basis then every linear bounded operator on E is a sum of two narrow operators. On the other hand, for the classical space E = L 1[0, 1] having no unconditional basis the sum of two narrow operators is a narrow operator. We show that a Köthe space on [0, 1] having “lots” of nonnarrow operators that are sum of two narrow operators need not have an unconditional basis. However, we do not know if such an r.i....
Some Properties of a Regular Sequence in Hilbert Space.
Some properties of -convexity.
Some properties of Banach-valued sequence spaces .
Some properties of basic sequences in Banach spaces.
Some properties of ,0 < p < 1
Some properties of spaces.
Some properties of monotone type multivalued operators in Banach spaces
Some properties of monotone type multivalued operators including accretive operators and the duality mapping are studied in connection with the structure of Banach spaces.
Some properties of Pythagorean modulus.
Some properties of the tensor product of Schwartz εb-spaces.
We define the ε-product of an εb-space by quotient bornological spaces and we show that if G is a Schwartz εb-space and E|F is a quotient bornological space, then their εc-product Gεc(E|F) defined in [2] is isomorphic to the quotient bornological space (GεE)|(GεF).
Some properties of the vector-valued Banach ideal space E(X) derived from those of E and X.
Some properties of weak Banach-Saks operators
We establish necessary and sufficient conditions under which weak Banach-Saks operators are weakly compact (respectively, L-weakly compact; respectively, M-weakly compact). As consequences, we give some interesting characterizations of order continuous norm (respectively, reflexive Banach lattice).
Some properties of weakly countably determined Banach spaces
Some properties of weighted Sobolev spaces in
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