共查询到20条相似文献,搜索用时 31 毫秒
1.
2.
Nguyen Quang Dieu Pham Hien Bang Nguyen Xuan Hong 《Journal of Mathematical Analysis and Applications》2014
Let u,v be m-subharmonic functions defined on a domain Ω in Cn. We are interested in giving sufficient conditions on u,v such that u=v on the whole domain Ω. Some applications to weak convergence of sequence of m-subharmonic functions are also discussed. 相似文献
3.
For a Tychonoff space X , we denote by Cp(X) and Cc(X) the space of continuous real-valued functions on X equipped with the topology of pointwise convergence and the compact-open topology respectively. Providing a characterization of the Lindelöf Σ-property of X in terms of Cp(X), we extend Okunev?s results by showing that if there exists a surjection from Cp(X) onto Cp(Y) (resp. from Lp(X) onto Lp(Y)) that takes bounded sequences to bounded sequences, then υY is a Lindelöf Σ-space (respectively K-analytic) if υX has this property. In the second part, applying Christensen?s theorem, we extend Pelant?s result by proving that if X is a separable completely metrizable space and Y is first countable, and there is a quotient linear map from Cc(X) onto Cc(Y), then Y is a separable completely metrizable space. We study also a non-separable case, and consider a different approach to the result of J. Baars, J. de Groot, J. Pelant and V. Valov, which is based on the combination of two facts: Complete metrizability is preserved by ?p-equivalence in the class of metric spaces (J. Baars, J. de Groot, J. Pelant). If X is completely metrizable and ?p-equivalent to a first-countable Y, then Y is metrizable (V. Valov). Some additional results are presented. 相似文献
4.
We present a uniqueness theorem for k -graph C?-algebras that requires neither an aperiodicity nor a gauge invariance assumption. Specifically, we prove that for the injectivity of a representation of a k -graph C?-algebra, it is sufficient that the representation be injective on a distinguished abelian C?-subalgebra. A crucial part of the proof is the application of an abstract uniqueness theorem, which says that such a uniqueness property follows from the existence of a jointly faithful collection of states on the ambient C?-algebra, each of which is the unique extension of a state on the distinguished abelian C?-subalgebra. 相似文献
5.
6.
We study the interplay of C?-dynamics and K -theory. Notions of chain recurrence for transformations groups (X,Γ) and MF actions for non-commutative C?-dynamical systems (A,Γ,α) are translated into K-theoretical language, where purely algebraic conditions are shown to be necessary and sufficient for a reduced crossed product to admit norm microstates. We are particularly interested in actions of free groups on AF algebras, in which case we prove that a K-theoretic coboundary condition determines whether or not the reduced crossed product is a matricial field (MF) algebra. One upshot is the equivalence of stable finiteness and being MF for these reduced crossed product algebras. 相似文献
7.
This is the sequel to Bhattacharjee et al. (in press) [3] where the notion of a p -extension of commutative rings was investigated: a unital extension of commutative rings, say R?S, is a p -extension if for every s∈S there is an r∈R such that rS=sS. In this article we apply the theory of p -extensions to rings of continuous functions. We show that this concept lays between the concepts of C?-embeddings and z-embeddings. 相似文献
8.
9.
10.
11.
We introduce the monotone Sokolov property and show that it is dual to monotone retractability in the sense that X is monotonically retractable if and only if Cp(X) is monotonically Sokolov. Besides, a space X is monotonically Sokolov if and only if Cp(X) is monotonically retractable. Monotone retractability and monotone Sokolov property are shown to be preserved by R-quotient images and Fσ-subspaces. Furthermore, every monotonically retractable space is Sokolov so it is collectionwise normal and has countable extent. We also establish that if X and Cp(X) are Lindelöf Σ-spaces then they are both monotonically retractable and have the monotone Sokolov property. An example is given of a space X such that Cp(X) has the Lindelöf Σ-property but neither X nor Cp(X) is monotonically retractable. We also establish that every Lindelöf Σ-space with a unique non-isolated point is monotonically retractable. On the other hand, each Lindelöf space with a unique non-isolated point is monotonically Sokolov. 相似文献
12.
Given n independent standard normal random variables, it is well known that their maxima Mn can be normalized such that their distribution converges to the Gumbel law. In a remarkable study, Hall proved that the Kolmogorov distance dn between the normalized Mn and its associated limit distribution is less than 3/log?n. In the present study, we propose a different set of norming constants that allow this upper bound to be decreased with dn≤C(m)/log?n for n≥m≥5. Furthermore, the function C(m) is computed explicitly, which satisfies C(m)≤1 and limm→∞?C(m)=1/3. As a consequence, some new and effective norming constants are provided using the asymptotic expansion of a Lambert W type function. 相似文献
13.
We give a constructive proof that any σ -porous subset of a Hilbert space has Lebesgue measure zero on typical C1 curves. Further, we discover that this result does not extend to all forms of porosity; we find that even power-p porous sets may meet many C1 curves in positive measure. 相似文献
14.
15.
16.
Given an arbitrarily weak notion of left-〈f〉-porosity and an arbitrarily strong notion of right-〈g〉-porosity, we construct an example of closed subset of R which is not σ -left-〈f〉-porous and is right-〈g〉-porous. We also briefly summarize the relations between three different definitions of porosity controlled by a function; we then observe that our construction gives the example for any combination of these definitions of left-porosity and right-porosity. 相似文献
17.
Motivated from [31], call a precompact group topology τ on an abelian group G ss-precompact (abbreviated from single sequence precompact ) if there is a sequence u=(un) in G such that τ is the finest precompact group topology on G making u=(un) converge to zero. It is proved that a metrizable precompact abelian group (G,τ) is ss-precompact iff it is countable. For every metrizable precompact group topology τ on a countably infinite abelian group G there exists a group topology η such that η is strictly finer than τ and the groups (G,τ) and (G,η) have the same Pontryagin dual groups (in other words, (G,τ) is not a Mackey group in the class of maximally almost periodic groups). 相似文献
18.
19.
In this article we apply a recently established transference principle in order to obtain the boundedness of certain functional calculi for semigroup generators. In particular, it is proved that if −A generates a C0-semigroup on a Hilbert space, then for each τ>0 the operator A has a bounded calculus for the closed ideal of bounded holomorphic functions on a (sufficiently large) right half-plane that satisfy f(z)=O(e−τRe(z)) as |z|→∞. The bound of this calculus grows at most logarithmically as τ↘0. As a consequence, f(A) is a bounded operator for each holomorphic function f (on a right half-plane) with polynomial decay at ∞. Then we show that each semigroup generator has a so-called (strong) m -bounded calculus for all m∈N, and that this property characterizes semigroup generators. Similar results are obtained if the underlying Banach space is a UMD space. Upon restriction to so-called γ-bounded semigroups, the Hilbert space results actually hold in general Banach spaces. 相似文献