A new result of G. A. Edgar on representing points in a convex bounded subset of Banach spaces with the Radon-Nikodym property as barycentres of Radon measures
A new type of orthogonality for normed planes
In this paper we introduce a new type of orthogonality for real normed planes which coincides with usual orthogonality in the Euclidean situation. With the help of this type of orthogonality we derive several characterizations of the Euclidean plane among all normed planes, all of them yielding also characteristic properties of inner product spaces among real normed linear spaces of dimensions .
A nondentable set without the tree property
A nonlinear Banach-Steinhaus theorem and some meager sets in Banach spaces
We establish a Banach-Steinhaus type theorem for nonlinear functionals of several variables. As an application, we obtain extensions of the recent results of Balcerzak and Wachowicz on some meager subsets of L¹(μ) × L¹(μ) and c₀ × c₀. As another consequence, we get a Banach-Mazurkiewicz type theorem on some residual subset of C[0,1] involving Kharazishvili's notion of Φ-derivative.
A normalized weakly null sequence with no shrinking subsequence in a Banach space not containing
A note about spaces.
A note of -basis
A note on absolutely P-summing operators.
A note on Banach algebras that are not isomorphic to a group algebra.
A note on Banach spaces and sub differentials of convex functions
A note on Banach spaces with -saturated duals
It is shown that there exists a Banach space with an unconditional basis which is not -saturated, but whose dual is -saturated.
A note on Banach spaces without the approximation property
A note on close-to-normal structure
A Note on compactness in Banach spaces.
A note on complex interpolation of Banach lattices
We complete a result of Hernandez on the complex interpolation for families of Banach lattices.
A note on complex -predual spaces.
A note on continuous restrictions of linear maps between Banach spaces.
A Note on cotype of smooth spaces.
A note on dual Banach spaces.
A note on Dunford-Pettis like properties and complemented spaces of operators
Equivalent formulations of the Dunford-Pettis property of order (), , are studied. Let , , , , and denote respectively the sets of all bounded linear, weakly compact, compact, unconditionally converging, and -convergent operators from to . Classical results of Kalton are used to study the complementability of the spaces and in the space , and of in and .