A Characterization of the Banach Spaces of Type p by Lévy Measures.
A differential equation related to the -norms
Let p ∈ (1,∞). The question of existence of a curve in ℝ₊² starting at (0,0) and such that at every point (x,y) of this curve, the -distance of the points (x,y) and (0,0) is equal to the Euclidean length of the arc of this curve between these points is considered. This problem reduces to a nonlinear differential equation. The existence and uniqueness of solutions is proved and nonelementary explicit solutions are given.
A Differential Inequality for the Distance Function in Normed Linear Spaces.
A few remarks on the results of Rosinski and Suchanecki concerning unconditional convergence and -sequences
A generalized -porous set with a small complement.
A geometric characterization of the Radon-Nikodym property in Banach spaces
A geometric version of the Moore theorem in the case of infinite dimensional Banach spaces.
A lower bound on the radius of analyticity of a power series in a real Banach space
Let F be a power series centered at the origin in a real Banach space with radius of uniform convergence ϱ. We show that F is analytic in the open ball B of radius ϱ/√e, and furthermore, the Taylor series of F about any point a ∈ B converges uniformly within every closed ball centered at a contained in B.
A method of reduction of constraints
A modification of Newton's method
A multiplier characterization of analytic UMD spaces
A new Expression of the Maximal Value of Banach Limits
A new proof of a Lemma by Phelps.
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 note on spaces of type
We show that a theorem of Rudin, concerning the sum of closed subspaces in a Banach space, has a converse. By means of an example we show that the result is in the nature of best possible.
A note on strong differentiability spaces
A note on the asymptotics of perturbed expanding maps.
A proof of admissibility of a class of random normed spaces
A proof of the Huff-Morris Radon-Nikodym theorem
A property of quasi-complements