On a metric on the space of monetary risk measures
We introduce a metric on the space of monetary risk measure, which generates the point-wise convergence topology and extends the metric on the initial compactum.
math.GN↗
arXiv subjects
A. A. Zaitov
Publications and source records attributed to A. A. Zaitov.
Order-Preserving Variants of The Basic Principles of Functional Analysis
We established order-preserving versions of the basic principles of functional analysis such as Hahn-Banach, Banach-Steinhaus, open mapping and Banach-Alaoglu theorems.
math.GN↗
Geometrical properties of the space $P_f(X)$ of probability measures
In this paper we prove that for a compact space $X$ inclusion $P_{f}(X)\in ANR$ holds if and only if $X\in ANR$. Further, it is shown that the functor $P_{f}$ preserves property of a compact to be $Q$-manifold or a Hilbert cube, properties of maps fibres to be $ANR$-compact, $Q$-manifold, Hilbert cube (the finite of Hilbert cube).
math.GN↗
Geometrical properties of space $I_f(X)$ of idempotent probability measures
In the paper we proved that for a compact $X$ inclusion $I_{f}(X)\in ANR$ holds if and only if $X\in ANR$. Further, it is shown that the functor $I_{f}$ preserves property of a compact to be $Q$-manyfold or a Hilbert cube, preserves property of map layers to be $ANR$-compact, compact $Q$-manyfold and a Hilbert cube (the finite sum of Hilbert cubes)
math.GN↗
On Čech-completeness of the space of order-preserving functionals
In this paper we establish that if a Tychonoff space $X$ is Čech-complete then the space $O_τ(X)$ of all $τ$-smooth order-preserving, weakly additive and normed functionals is also Čech-complete
math.GN↗
On perfect metrizability of the functor of idempotent probability measures
In this paper we establish that the functor of idempotent probability measures acting in the category of compacta and their continuous mappings is perfect metrizable.
math.GN↗
Algebras of unbounded operators over the ring of measurable functions and their derivations and automorphisms
In the present paper derivations and *-automorphisms of algebras of unbounded operators over the ring of measurable functions are investigated and it is shown that all L^0-linear derivations and L^{0}-linear *-automorphisms are inner. Moreover, it is proved that each L^0-linear automorphism of the algebra of all linear operators on a bo-dense submodule of a Kaplansky-Hilbert module over the ring of measurable functions is spatial.
math.FA↗
On the weight and the density of the space of order-preserving functionals
In the present paper it is proved that the functors $O_τ$ of $τ$-smooth order preserving functionals and $O_R$ of Radon order preserving functionals preserve the weight of infinite Tychonoff spaces. Moreover, it is established that the density and the weak density of infinite Tychonoff spaces do not increase under these functors.
math.GN↗