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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...
An Elementary Proof of Komlos-Révész Theorem in Hilbert Spaces
Convergence Hilbert space Komlos Révész
2009/2/5
We provide an elementary proof of Komlos-Révész theorem in Hilbert spaces.
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...
Separation by Hyperplanes in Finite-Dimensional Vector Spaces over Archimedean Ordered Fields
archimedean field finite-dimensional vector space convex set s-closed separation support convex function epigraph optimization
2009/1/23
Theorems on the separation of convex sets by hyperplanes are among the basic tools of convex analysis and mathematical programming. The main results of the present paper are new (and in a sense best p...
Denting Points in Bochner Banach Ideal Spaces X(E)
Denting Points Bochner Banach Ideal Spaces X(E)
2009/1/20
Let $(X, \|.\|_{X})$ be an order-continuous Banach ideal space over a $\sigma-$ finite measure space $(\Omega,\Sigma,\mu)$ and $E$ a Banach space. We prove that a function $f$ of the vector Banach ide...
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...
Some Geometric Properties in Orlicz Sequence Spaces equipped with Orlicz Norm
Orlicz sequence space rotundity local uniform rotundity compact local uniform rotundity property H smoothness copy of $l_\infty$
2009/1/20
It is proved that for any reflexive Banach space $X$, both $X$ and $X^{*}$ are CLUR if and only if both $X$ and $X^{*}$ have property H. Criteria for rotundity, local uniform rotundity, compact l...
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 ...
Epi-Distance Convergence of Parametrised Sums of Convex Functions in Non-Reflexive Spaces
Epi-Distance Convergence Parametrised Sums Convex Functions Non-Reflexive Spaces
2009/1/13
A weakened set of conditions is established for the epi-distance convergence of a sum $\{f_v+g_v\}_{v\in W}$ of parametrised closed convex functions $\{f_v\}_{v\in W}$ and $\{g_v\}_{v\in W}$ for $v\to...
Interpolation of Ideal Measures by Abstract $K$ and $J$ Spaces
real interpolation ideal measures operator ideals shift operators
2007/12/10
We work with the abstract K and J interpolation method generated by a sequence lattice $\Gamma$. We investigate the deviation of an interpolated operator from a given operator ideal by establishing fo...