On the generalized Roper-Suffridge extension operator in Banach spaces.
On the geometric characterization of differentiability. I.
On the geometric characterization of differentiability. II.
On the geometrical structure of Lebesgue nullsets
On the geometry of Banach spaces with modulus of convexity of power type 2
We use one-dimensional differential inequalities to estimate the squareness and type of Banach spaces with modulus of convexity of power type two. The estimates obtained are sharp and the constants involved moderate.
On the geometry of and .
On the Geometry of Positive Maps in Matrix Algebras.
On the geometry of proportional quotients of
We compare various constructions of random proportional quotients of (i.e., with the dimension of the quotient roughly equal to a fixed proportion of m as m → ∞) and show that several of those constructions are equivalent. As a consequence of our approach we conclude that the most natural “geometric” models possess a number of asymptotically extremal properties, some of which were hitherto not known for any model.
On the geometry of spaces of K-valued operators
On the Geometry of Stable Compact Convex Sets.
On the geometry of the unit ball of a C*- algebra.
On the Glicksberg theorem for locally quasi-convex Schwartz groups
We prove that every locally quasi-convex Schwartz group satisfies the Glicksberg theorem for weakly compact sets.
On the global stable manifold
We give an alternative proof of the stable manifold theorem as an application of the (right and left) inverse mapping theorem on a space of sequences. We investigate the diffeomorphism class of the global stable manifold, a problem which in the general Banach setting gives rise to subtle questions about the possibility of extending germs of diffeomorphisms.
On the Gram-Schmidt orthonormalizatons of subsystems of Schauder systems
In one of the earliest monographs that involve the notion of a Schauder basis, Franklin showed that the Gram-Schmidt orthonormalization of a certain Schauder basis for the Banach space of functions continuous on [0,1] is again a Schauder basis for that space. Subsequently, Ciesielski observed that the Gram-Schmidt orthonormalization of any Schauder system is a Schauder basis not only for C[0,1], but also for each of the spaces , 1 ≤ p < ∞. Although perhaps not probable, the latter result would...
On the graph of a quasi-additive function.
On the growth of analytic semigroups along vertical lines
We construct two Banach algebras, one which contains analytic semigroups such that arbitrarily slowly as , the other which contains ones such that arbitrarily fast
On the -property of some Banach sequence spaces
In this paper we define a generalized Cesàro sequence space and consider it equipped with the Luxemburg norm under which it is a Banach space, and we show that the space posses property (H) and property (G), and it is rotund, where is a bounded sequence of positive real numbers with for all .
On the Hahn-Banach theorem
On the Hardy-type integral operators in Banach function spaces.
Characterization of the mapping properties such as boundedness, compactness, measure of non-compactness and estimates of the approximation numbers of Hardy-type integral operators in Banach function spaces are given.
On the Hausdorff-Young Theorem for Amalgams.