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On removability properties of $ψ$-uniform domains in Banach spaces
Uniform domain uniform domain removability property quasihyperbolic metric
2012/6/9
Suppose that $E$ and $E'$ denote real Banach spaces with the same dimension at least 2. The main aim of this paper is to show that a domain $D$ in $E$ is a $\psi$-uniform domain if and only if $D\back...
Minimization of Nonsmooth Convex Functionals in Banach Spaces
Banach spaces nonsmooth optimization subgradient methods metric projection generalized projection weak convergence
2009/2/5
We develop a unified framework for convergence analysis of subgradient and subgradient projection methods for minimization of nonsmooth convex functionals in Banach spaces. The important novel featu...
Unbounded Linear Monotone Operators on Nonreflexive Banach Spaces
Linear Monotone Operators Nonreflexive Banach Spaces
2009/1/23
This study of unbounded linear monotone operators $T\colon E \to E^*$ for nonreflexive Banach spaces $E$ was motivated by the (still open) problem of distinguishing between several well-studied classe...
The Distribution of Unbounded Random Sets and the Multivalued Strong Law of Large Numbers in Nonreflexive Banach Spaces
distribution of random sets multivalued strong law of large numbers set convergence measurable multifunctions convex sets
2009/1/20
In the first part, we introduce appropriate tools concerning the distribution of random sets. We study the relation between the distribution of a random set, whose values are closed subsets of a Banac...
Total Convexity for Powers of the Norm in Uniformly Convex Banach Spaces
Uniformly Convex Banach Spaces Norm Total Convexity
2009/1/13
The aim of the paper is to show that, in uniformly convex Banach spaces, the powers of the norm with exponent r > 1 share a property called total convexity. Using this fact we establish a formula for ...