We study some structural aspects of the subspaces of the non-commutative (Haagerup) Lp-spaces associated with a general (non necessarily semi-finite) von Neumann algebra a. If a subspace X of Lp(a) contains uniformly the spaces lnp , n ≥ 1, it contains an almost isometric, almost 1-complemented copy of lp. If X contains uniformly the finite dimensional Schatten classes S p , it contains their l...

In summability theory, de la Vallée-Poussin’s mean is first used to define the (V, λ)-summability by Leindler [9]. Malkowsky and Savaş [14] introduced and studied some sequence spaces which arise from the notion of generalized de la ValléePoussin mean. Also the (V, λ)-summable sequence spaces have been studied by many authors including [6] and [20]. Recently, there has been a lot of interest in...

Let K be a nonempty closed convex nonexpansive retract of a uniformly convex Banach space E with P as a nonexpansive retraction. Let T : K → E be non-self asymptotically nonexpansive in the intermediate sense mapping with F (T ) 6= φ. Let {α n }, {β n } and {γ n } are sequences in [0, 1] with α (i) n + β (i) n + γ (i) n = 1 for all i = 1, 2, . . . , N . From arbitrary x1 ∈ K, define the sequenc...

The Hahn-Banach theorem states that onto each line in every normed space, there is a unitary projection, and Kadec and Snobar [KS71] proved (using John’s ellipsoid) that onto each n-dimensional subspace of any real normed space, there is a projection with norm at most λn 6 √ n . Grünbaum [Grü60] conjectured that λ2 = 4/3 = 1.333... < 1.414... = √ 2 , which is the projection constant of the plan...

Suppose K is a nonempty closed convex nonexpansive retract of a real uniformly convex Banach space E with P as a nonexpansive retraction. Let T : K → E be an asymptotically nonexpansive mapping with {kn} ⊂ [1,∞) such that ∑∞ n=1(kn − 1) <∞ and F(T) is nonempty, where F(T) denotes the fixed points set of T . Let {αn}, {α′n}, and {α′′ n } be real sequences in (0,1) and ≤ αn,α′n,α′′ n ≤ 1− for all...

Those kinds of infinite direct sums are characterized for which NUC (NUS, respectively) is inherited from the component spaces to the direct sum. 1. NUC and the lower KK-modulus. The Banach space X is said to be nearly uniformly convex, abbreviated NUC (cf. [2]), if: for every ε > 0, there exists δ > 0 such that the convex hull conv{xn} of every sequence {xn} in the unit ball BX of X with separ...

A Banach space has the weak fixed point property if its dual space has a weak∗ sequentially compact unit ball and the dual space satisfies the weak∗ uniform Kadec-Klee property; and it has the fixed point property if there exists ε > 0 such that, for every infinite subset A of the unit sphere of the dual space, A ∪ (−A) fails to be (2 − ε)-separated. In particular, E-convex Banach spaces, a cla...

Abstract In this paper, we are interested in giving two characterizations for the so-called property L $$_{o,o}$$ o , , a local vector valued Bollobás type theorem. We say that ( X Y ) has whenever given $$\varepsilon &gt; 0$$ <mml:mi...

and Applied Analysis 3 for each x, y ∈ U. It is also said to be uniformly smooth if the limit is attainted uniformly for each x, y ∈ U. It is well known that ifE is smooth, then the dualitymapping J is single valued. It is also known that if E is uniformly smooth, then J is uniformly norm-to-norm continuous on each bounded subset ofE. Someproperties of the dualitymapping have been given in [22]...