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1.
Let X be a Banach space, K be a scattered compact and T: B C(K)X be a Fréchet smooth operator whose derivative is uniformly continuous. We introduce the smooth biconjugate T**: B C(K)**X** and prove that if T is noncompact, then the derivative of T** at some point is a noncompact linear operator. Using this we conclude, among other things, that either is compact or that ℓ1 is a complemented subspace of X*. We also give some relevant examples of smooth functions and operators, in particular, a C 1,u -smooth noncompact operator from B c O which does not fix any (affine) basic sequence. P. Hájek was supported by grants A100190502, Institutional Research Plan AV0Z10190503.  相似文献   

2.
In this paper, we introduce a new class of sets and a new class of functions called geodesic E-convex sets and geodesic E-convex functions on a Riemannian manifold. The concept of E-quasiconvex functions on R n is extended to geodesic E-quasiconvex functions on Riemannian manifold and some of its properties are investigated. Afterwards, we generalize the notion of epigraph called E-epigraph and discuss a characterization of geodesic E-convex functions in terms of its E-epigraph. Some properties of geodesic E-convex sets are also studied.  相似文献   

3.
We investigate E*-dense semi\-groups as analogues of E-densesemigroupsfor semigroups with zero. We give a characterisation theorem forE*-dense semigroups whose idempotents form a *-rectangularband. The construction methods of generalised Rees matrix semigroupsare employed to provide examples and illustrations. Our results areanalogous to those of Weipoltshammer for E-dense semigroups.  相似文献   

4.
We define K-homology groups K * () for small C * -categories in terms of Hilbert modules over the C * -category . We also define a functor A f from the category of small C * -categories into the category of C * -algebras and show that there is a natural isomorphism . In addition, we give an easy construction of a functor from the category of C * -algebras into the category of symmetric spectra which represents K-homology, i.e. we show that the functor comes with a natural isomorphism for C * -algebras A. It then follows that the composition A f provides a functor that can be used in the Davis-Lück approach for constructing the Baum-Connes map.  相似文献   

5.
This paper is devoted to strict K-monotonicity and K-order continuity in symmetric spaces. Using a local approach to the geometric structure in a symmetric space E we investigate a connection between strict K-monotonicity and global convergence in measure of a sequence of the maximal functions. Next, we solve an essential problem whether an existence of a point of K-order continuity in a symmetric space E on \([0,\infty )\) implies that the embedding \(E\hookrightarrow {L^1}[0,\infty )\) does not hold. We present a complete characterization of an equivalent condition to K-order continuity in a symmetric space E using a notion of order continuity and the fundamental function of E. We also investigate a relationship between strict K-monotonicity and K-order continuity in symmetric spaces and show some examples of Lorentz spaces and Marcinkiewicz spaces having these properties or not. Finally, we discuss a local version of a crucial correspondence between order continuity and the Kadec–Klee property for global convergence in measure in a symmetric space E.  相似文献   

6.
Using group congruences, we obtain necessary and sufficient conditions for an ordered E-inversive semigroup to be a Dubreil-Jacotin semigroup. We also determine when such a semigroup is naturally ordered. In particular, when the subset of regular elements is a subsemigroup it contains a multiplicative inverse transversal.  相似文献   

7.
Let k be a field and E(n) be the 2 n+1-dimensional pointed Hopf algebra over k constructed by Beattie, Dăscălescu and Grünenfelder [J. Algebra, 2000, 225: 743–770]. E(n) is a triangular Hopf algebra with a family of triangular structures R M parameterized by symmetric matrices M in M n (k). In this paper, we study the Azumaya algebras in the braided monoidal category $ E_{(n)} \mathcal{M}^{R_M } $ E_{(n)} \mathcal{M}^{R_M } and obtain the structure theorems for Azumaya algebras in the category $ E_{(n)} \mathcal{M}^{R_M } $ E_{(n)} \mathcal{M}^{R_M } , where M is any symmetric n×n matrix over k.  相似文献   

8.
We verify a conjecture of Rognes by establishing a localization cofiber sequence of spectra \(K(\mathbb{Z})\to K(ku)\to K(KU) \to\Sigma K(\mathbb{Z})\) for the algebraic K-theory of topological K-theory. We deduce the existence of this sequence as a consequence of a dévissage theorem identifying the K-theory of the Waldhausen category of finitely generated finite stage Postnikov towers of modules over a connective \(A_\infty\) ring spectrum R with the Quillen K-theory of the abelian category of finitely generated \(\pi_{0}R\)-modules.  相似文献   

9.
Let λK m,n be a complete bipartite multigraph with two partite sets having m and n vertices, respectively. A K p,q -factorization of λK m,n is a set of edge-disjoint K p,q -factors of λK m,n which partition the set of edges of λK m,n . When p = 1 and q is a prime number, Wang, in his paper [On K 1,q -factorization of complete bipartite graph, Discrete Math., 126: (1994), 359-364], investigated the K 1,q -factorization of K m,n and gave a sufficient condition for such a factorization to exist. In papers [K 1,k -factorization of complete bipartite graphs, Discrete Math., 259: 301-306 (2002),; K p,q -factorization of complete bipartite graphs, Sci. China Ser. A-Math., 47: (2004), 473-479], Du and Wang extended Wang’s result to the case that p and q are any positive integers. In this paper, we give a sufficient condition for λK m,n to have a K p,q -factorization. As a special case, it is shown that the necessary condition for the K p,q -factorization of λK m,n is always sufficient when p : q = k : (k + 1) for any positive integer k.  相似文献   

10.
11.
We define and investigate separable K-linear categories. We show that such a category C is locally finite and that every left C-module is projective. We apply our main results to characterize separable linear categories that are spanned by groupoids or delta categories.  相似文献   

12.
Erik A. van Doorn 《TOP》2011,19(2):336-350
We consider the M/M/N/N+R service system, characterized by N servers, R waiting positions, Poisson arrivals and exponential service times. We discuss representations and bounds for the rate of convergence to stationarity of the number of customers in the system, and study its behaviour as a function of RN and the arrival rate λ, allowing λ to be a function of N.  相似文献   

13.
We show that if K is a compact metric space then C(K) is a 2-absolute Lipschitz retract. We then study the best Lipschitz extension constants for maps into C(K) from a given metric space M, extending recent results of Lancien and Randrianantoanina. They showed that a finite-dimensional normed space which is polyhedral has the isometric extension property for C(K)-spaces; here we show that the same result holds for spaces with Gateaux smooth norm or of dimension two; a three-dimensional counterexample is also given. We also show that X is polyhedral if and only if every subset E of X has the universal isometric extension property for C(K)-spaces. We also answer a question of Naor on the extension of Hölder continuous maps.  相似文献   

14.
Let O n be the order-preserving transformation semigroup on X n . For an arbitrary integer r such that 1≤rn−2, we completely describe the maximal regular subsemibands of the semigroup K(n,r)={αO n :|im(α)|≤r}. We also formulate the cardinal number of such subsemigroups.  相似文献   

15.
For an MV-algebra let J 0( ) be the system of all closed ideals of ; this system is partially ordered by the set-theoretical inclusion. A radical class X of MV-algebras will be called a K-radical class iff, whenever ∈ X and is an MV-algebra with J 0( ) ≅ J 0( ), then ∈ X. An analogous notation for lattice ordered groups was introduced and studied by Conrad. In the present paper we show that there is a one-to-one correspondence between K-radical classes of MV-algebras and K-radical classes of abelian lattice ordered groups. We also prove an analogous result for product radical classes of MV-algebras; product radical classes of lattice ordered groups were studied by Ton. This work has been partially supported by the Slovak Academy of Sciences via the project Center of Excellence-Physics of Information, Grant I/2/2005.  相似文献   

16.
Let M n (K) be the algebra of all n × n matrices over an infinite field K. This algebra has a natural ℤ n -grading and a natural ℤ-grading. Finite bases for its ℤ n -graded identities and for its ℤ-graded identities are known. In this paper we describe finite generating sets for the ℤ n -graded and for the ℤ-graded central polynomials for M n (K) Partially supported by CNPq 620025/2006-9  相似文献   

17.
Erdös et al and Gerencsér et al had shown that in any 2-edge-coloring of K 3n-1, there is a n-matching containing edges with the same color(we call such matching monochromatic matching). In this paper we show that for any 2-edge-coloring of K 3n-1 there exists a monochromatic subgraph H of K 3n-1 which contains exponentially many monochromatic n-matchings.  相似文献   

18.
Approximation formulae are suggested for the mean and variance of customers in M/E n /s queues. It is shown that the distributions can be approximated by using the mean and variance to fit Gamma functions. A brief comment on the more general E m /E n /s case is given.  相似文献   

19.
In this note, we find a monomial basis of the cyclotomic Hecke algebra \({\mathcal{H}_{r,p,n}}\) of G(r,p,n) and show that the Ariki-Koike algebra \({\mathcal{H}_{r,n}}\) is a free module over \({\mathcal{H}_{r,p,n}}\), using the Gröbner-Shirshov basis theory. For each irreducible representation of \({\mathcal{H}_{r,p,n}}\), we give a polynomial basis consisting of linear combinations of the monomials corresponding to cozy tableaux of a given shape.  相似文献   

20.
For the multi-channel bulk-arrival queue, M x /M/c, Abol'nikov and Kabak independently obtained steady state results. In this paper the results of these authors are extended, corrected and simplified. A number of measures of efficiency are calculated for three cases where the arrival group size has: (i) a constant value, (ii) a geometric distribution, or (iii) a positive Poisson distribution. The paper also shows how to calculate fractiles for both the queue length and the waiting time distribution. Examples of extensive numerical results for certain measures of efficiency are presented in tabular and chart form.  相似文献   

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