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
Weak uniform continuity and weak sequential continuity of continuous n-linear mappings between Banach spaces.
In this paper it is shown that the class LnWU (E1,E2,...,En;F) of weakly uniformly continuous n-linear mappings from E1x E2x...x En to F on bounded sets coincides with the class LnWSC (E1,E2,...,En;F) of weakly sequentially continuous n-linear mappings if and only if for every Banach space F, each Banach space Ei for i = 1,2,...,n does not contain a copy of l1.
Weak uniform normal structure and iterative fixed points of nonexpansive mappings
This paper is concerned with weak uniform normal structure and iterative fixed points of nonexpansive mappings. Precisely, in Section 1, we show that the geometrical coefficient β(X) for a Banach space X recently introduced by Jimenez-Melado [8] is exactly the weakly convergent sequence coefficient WCS(X) introduced by Bynum [1] in 1980. We then show in Section 2 that all kinds of James' quasi-reflexive spaces have weak uniform normal structure. Finally, in Section 3, we show that in a space X with...
Weak uniform normal structure in direct sum spaces
The weak normal structure coefficient WCS(X) is computed or bounded when X is a finite or infinite direct sum of reflexive Banach spaces with a monotone norm.
Weak uniform rotundity in Orlicz spaces
Weak uniform rotundity of Musielak--Orlicz spaces
We give necessary and sufficient conditions for weak uniform rotundity of Musielak–Orlicz spaces with the Luxemburg norm. The result is a generalization of a theorem by Kami’nska and Kurc.
Weak vs. norm compactness in : the Bocce criterion
Weakly almost periodic solutions of linear equations in Banach spaces
Weakly amenable groups and the RNP for some Banach algebras related to the Fourier algebra
It is shown that if G is a weakly amenable unimodular group then the Banach algebra , where is the Figà-Talamanca-Herz Banach algebra of G, is a dual Banach space with the Radon-Nikodym property if 1 ≤ r ≤ max(p,p’). This does not hold if p = 2 and r > 2.
Weakly Compact Generating and Shrinking Markusevic Bases
2000 Mathematics Subject Classification: 46B30, 46B03.It is shown that most of the well known classes of nonseparable Banach spaces related to the weakly compact generating can be characterized by elementary properties of the closure of the coefficient space of Markusevic bases for such spaces. In some cases, such property is then shared by all Markusevic bases in the space.
Weakly Compact Operators and the Dunford-Pettis Property on Uniform Spaces
Weakly compact sets in Orlicz sequence spaces
We combine the techniques of sequence spaces and general Orlicz functions that are broader than the classical cases of -functions. We give three criteria for the weakly compact sets in general Orlicz sequence spaces. One criterion is related to elements of dual spaces. Under the restriction of , we propose two other modular types that are convenient to use because they get rid of elements of dual spaces. Subsequently, by one of these two modular criteria, we see that a set in Riesz spaces ...