Weak compactness and Orlicz spaces
We give new proofs that some Banach spaces have Pełczyński's property (V).
Weak compactness and summability
Weak compactness and σ-Asplund generated Banach spaces
σ-Asplund generated Banach spaces are used to give new characterizations of subspaces of weakly compactly generated spaces and to prove some results on Radon-Nikodým compacta. We show, typically, that in the framework of weakly Lindelöf determined Banach spaces, subspaces of weakly compactly generated spaces are the same as σ-Asplund generated spaces. For this purpose, we study relationships between quantitative versions of Asplund property, dentability, differentiability, and of weak compactness...
Weak compactness in the dual of a C*-algebra is determined commutatively.
Weak completeness in spaces of operators
Weak continuity of holomorphic automorphisms in JB-triples.
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 and weighted averages for groups of operators
Weak convergence in infinite dimensional spaces
Weak countable compactness implies quasi-weak drop property
Every weakly countably compact closed convex set in a locally convex space has the quasi-weak drop property.
Weak Distances between Random Subproportional Quotients of
Lower estimates for weak distances between finite-dimensional Banach spaces of the same dimension are investigated. It is proved that the weak distance between a random pair of n-dimensional quotients of is greater than or equal to c√(n/log³n).
Weak fixed point property and Banach lattices
Weak Grothendieck's theorem.
Weak Kato-Inequalities and Positive Semigroups.
Weak moduli of convexity.
Let E be a real normed linear space with unit ball B and unit sphere S. The classical modulus of convexity of J. A. Clarkson [2] δE(ε) = inf {1 - 1/2||x + y||: x,y ∈ B, ||x - y|| ≥ ε} (0 ≤ ε ≤ 2)is well known and it is at the origin of a great number of moduli defined by several authors. Among them, D. F. Cudia [3] defined the directional, weak and directional weak modulus of convexity of E, respectively, asδE(ε,g) = inf {1 - 1/2||x + y||: x,y ∈ B, g(x-y) ≥ ε}δE(ε,f) = inf {1 - 1/2 f(x,y): x,y...
Weak-norm sequentially continuous operators
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 precompactness and property (V*) in spaces of compact operators
We give sufficient conditions for subsets of compact operators to be weakly precompact. Let (resp. ) denote the set of all w* - w continuous (resp. w* - w continuous compact) operators from E* to F. We prove that if H is a subset of such that H(x*) is relatively weakly compact for each x* ∈ E* and H*(y*) is weakly precompact for each y* ∈ F*, then H is weakly precompact. We also prove the following results: If E has property (wV*) and F has property (V*), then has property (wV*). Suppose...
Weak sequential completeness of sequence spaces.
Köthe and Toeplitz introduced the theory of sequence spaces and established many of the basic properties of sequence spaces by using methods of classical analysis. Later many of these same properties of sequence spaces were reestablished by using soft proofs of functional analysis. In this note we would like to point out that an improved version of a classical lemma of Schur due to Hahn can be used to give very short proofs of two of the weak sequential completeness results of Köthe and Toeplitz....
Weak star and bounded weak star continuity of Banach algebra products