Uniform convexity of Banach spaces l({p_{i}})
Uniform extension of linear functionals
Uniformly convex norms in spaces with unconditional basis
Uniformly convex norms on Banach lattices
Uniformly non- and B-convex Banach spaces
Uniformly smooth partitions of unity on superreflexive Banach spaces
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Upper and lower estimates in Banach sequence spaces
Here we study the existence of lower and upper -estimates of sequences in some Banach sequence spaces. We also compute the sharp estimates in their basis. Finally, we give some applications to weak sequential continuity of polynomials.
-basic sequences and reflexivity of Banach spaces
We observe that a separable Banach space is reflexive iff each of its quotients with Schauder basis is reflexive. Similarly if is not reflexive for reflexive and then is is not reflexive for some , having a basis.
Weak* bases in conjugate Banach spaces
Weak compact generating in duality
Weak Convergence and Weak Convergence
In this article, we deal with weak convergence on sequences in real normed spaces, and weak* convergence on sequences in dual spaces of real normed spaces. In the first section, we proved some topological properties of dual spaces of real normed spaces. We used these theorems for proofs of Section 3. In Section 2, we defined weak convergence and weak* convergence, and proved some properties. By RNS_Real Mizar functor, real normed spaces as real number spaces already defined in the article [18],...
Weak convergence in infinite dimensional spaces
Weak orthogonality and weak property () in some Banach sequence spaces
It is proved that a Köthe sequence space is weakly orthogonal if and only if it is order continuous. Criteria for weak property () in Orlicz sequence spaces in the case of the Luxemburg norm as well as the Orlicz norm are given.
Weak star and bounded weak star continuity of Banach algebra products
Weakly continuous functions of Baire class 1.
For a compact Hausdorff space K and a Banach space X, let WC(K,X) denote the space of X-valued functions defined on K, that are continuous when X has the weak topology. In this note by a simple Banach space theoretic argument, we show that given f belonging to WC(K,X) there exists a net {fa} contained in C(K,X) (space of norm continuous functions) such that fa --> f pointwise w.r.t. the norm topology on X. Such a function f is said to be of Baire class 1.
Zur Stetigkeit der mengenwertigen metrischen Projektion in endlichdimensionalen Räumen.
Двойственные банаховы пары
Задача Хелли и наилучшее приближение суммируемых функций
Изоморфизмы и проекции для фактопространств -пространств по их рефлексивным подпространствам