All posts under category "Mathematics / Math.FA"
The objects of the Dranishnikov asymptotic category are proper metric spaces and the morphisms are asymptotically Lipschitz maps. In this paper we provide an example of an asymptotically zero-dimensional space (in the sense of Gromov) whose space of compact convex subsets of probability measures is
Let $X$ be a Borel subset of the Cantor set textbf{C} of additive or multiplicative class ${alpha},$ and $f: X to Y$ be a continuous function with compact preimages of points onto $Y subset textbf{C}.$ If the image $f(U)$ of every clopen set $U$ is the intersection of an open and a closed set, then
The close relation between properness and closedness of maps is well-known. For instance, for Fredholm mappings of infinite dimensional Banach manifolds, these properties are equivalent. On the other hand, properness of maps plays an important role for construction of various topological degree theo
Assuming $mathfrak p=mathfrak c$, we show that for every Eberlein compact space $L$ of weight $mathfrak c$ there exists a short exact sequence $0to c_0to Xto C(L)to 0$, where the Banach space $X$ is not isomorphic to a $C(K)$-space.
The paper investigates the variation of the spectrum of operators in infinite dimensional Banach spaces. In particular, it is shown that the spectrum function is Borel from the space of bounded operators on a separable Banach space; equipped with the strong operator topology, into the Polish space o
Let $mathcal{A}$ be an algebra, and let $mathcal{A}^2 =$ span${ab : a, b in mathcal{A}}$ be a subalgebra of $mathcal{A}$. In this paper, we prove that if $mathcal{A}^2$ has infinite codimension in $mathcal{A}$ iff $mathcal{A}$ has discontinuous square annihilation property (DSAP). In fact, in this c
A reproducing kernel Hilbert space (RKHS) has four well-known easily derived properties. Since these properties are usually not emphasized as a simple means of gaining insight into RKHS structure, they are singled out and proved in this brief article.
A space X is finite dimensional, locally compact and separable metrizable if and only if X has a finite basic family: continuous functions Phi_1,...,Phi_n of X to the reals, R, such that for all continuous f from X to R there are g_1,..., g_n in C(R) satisfying f(x)=g_1(Phi_1(x))+g_2(Phi_2(x))+...+g
We strengthen the property $Delta$ of a function $f:[omega_2]^2rightarrow [omega_2]^{leq omega}$ considered by Baumgartner and Shelah. This allows us to consider new types of amalgamations in the forcing used by Rabus, Juh'asz and Soukup to construct thin-very tall compact scattered spaces. We consi
Extending and unifying concepts extensively used in the literature, we introduce the notion of approximable interpolation sets for algebras of functions on locally compact groups, especially for weakly almost periodic functions and for uniformly continuous functions. We characterize approximable int
We show that character analysis using Fourier series is possible, at least when a mathematical character is considered. Previous approaches to character analysis are somewhat not in the spirit of harmonic analysis.
We give an explicit (in particular, deterministic polynomial time) construction of subspaces X of R^N of dimension (1-o(1))N such that for every element x in X, |x|_1 and N^{1/2} |x|_2 are equivalent up to a factor of (log N)^{log log log N}. If we are allowed to use N^{o(1)} random bits, this facto
We show that a family of quantum Ornstein-Uhlenbeck semigroups is hypercontractive. We also obtain the optimal order of the optimal time up to a constant for those elements whose Gibbs state is zero. The main ingredient of our proof is Meixiner polynomials.
Two-points nonlocal problem for the first order differential evolution equation with an operator coefficient in a Banach space $X$ is considered. An exponentially convergent algorithm is proposed and justified in assumption that the operator coefficient is strongly positive and some existence and un
In this paper we first generalize the Ostrowski inequality on time scales for k points and then unify corresponding continuous and discrete versions. We also point out some particular Ostrowski type inequalities on time scales as special cases.
In this paper we first extend a generalization of Ostrowski type inequality on time scales for functions whose derivatives are bounded and then unify corresponding continuous and discrete versions. We also point out some particular integral type inequalities on time scales as special cases.
In the present paper it is proved that the functors $O_tau$ of $tau$-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
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