摘要:

Let Λ be a scalar sequence space which is endowed with a normal locally convex topology. For a separated locally convex space E we denote by Λ(E) the vector space of all sequences g in E for which (>g(i),a<) ε Λ for all a ε E'. We define a locally convex topology ζ on Λ(E) and then characterize the dual of the ζ-closure (denoted by Λc(E)) of the finite sequences in Λ(E). We demonstrate the existence of a continuous projection from Λ(E)' onto a subspace of Λ(E)' which is isomorphic to Λc(E)'. Furthermore, we find a topological decomposition of Λαc(E)”, where one of the factors is isomorphic to Λ;α(E). These results are then applied to find necessary and sufficient conditions for Λα(E) to be semi-reflexive. A parallel development yields the same results for the space Λ(E') of all sequences f in E' for which (>x, f(i)<) ε Λ; for all x ε E, when E is barrelled. We conclude the paper by application of the results on vector sequence spaces to spaces of operators—including for instance, necessary and sufficient conditions for Lb(E,Λ;) and Lb(Λ,E) to be semi-reflexive.

ISSN:1607-3606    

DOI:10.1080/16073606.1985.9631919

出版商:Taylor & Francis Group    

年代:1985

数据来源: Taylor

摘要:

In this paper we prove the existence of a free approximation to any chain complex (not necessarily bounded) over any ring whatsoever.

ISSN:1607-3606    

DOI:10.1080/16073606.1985.9631920

出版商:Taylor & Francis Group    

年代:1985

数据来源: Taylor

摘要:

Let S be a subset of the vertex set V(G) of a nontrivial connected graph G. The geodetic closure (S) of S is the set of all vertices on geodesics between two vertices in S. The first player A chooses a vertex v1of G. The second player B then picks v2≠ v1and forms the geodetic closure (S2) = ({v1, v2}). Now A selects v3ε V—S2and forms (S3) = ({v1, v2, v3}), etc. The player who first selects a vertex vnsuch that (Sn) = V wins the achievement game, but loses the avoidance game. These geodetic achievement and avoidance games are solved for several families of graphs by determining which player is the winner.

ISSN:1607-3606    

DOI:10.1080/16073606.1985.9631921

出版商:Taylor & Francis Group    

年代:1985

数据来源: Taylor

摘要:

Answering to a question formulated by A.F. MONNA, we study the Hahn-Banach extension property and other related topics within the context of A-normed spaces over valued fields.

ISSN:1607-3606    

DOI:10.1080/16073606.1985.9631922

出版商:Taylor & Francis Group    

年代:1985

数据来源: Taylor

摘要:

The Hardy, Littlewood, Polya class of power means (wiza1+ …+wnzan)1/a, including the usual harmonic, geometric, and arithmetic mean values, has been generalized by Bruno deFinetti and B. C. Carlson. These two generalizations are here simultaneously extended to a comprehensive generalized mean value involving an arbitrary continuous strictly monotonic function and a linear form in the data values with Dirichlet-distributed coefficients. Properties are given which relate the new mean naturally to its deFinetti and Carlson subclasses. Statistical interpretations and possible further extensions arc discussed.

ISSN:1607-3606    

DOI:10.1080/16073606.1985.9631923

出版商:Taylor & Francis Group    

年代:1985

数据来源: Taylor

摘要:

Herrlich and Strecker [9] give examples of monotopological categories for which the MacNeille completion coincides with the universal initial completion. It is shown here that this situation always holds for monotopological categories. If the category is a proper monotopological c-category, then the MacNeille completion also coincides with the largest epi-reflective initial completion. During the course of the proof a lemma is given which characterizes monotopological categories (not necessarily c-categories) which are already topological. (Schwarz [14] gave such a characterization for the case of c-categories.)

ISSN:1607-3606    

DOI:10.1080/16073606.1985.9631924

出版商:Taylor & Francis Group    

年代:1985

数据来源: Taylor

摘要:

A connected, nontrivial, simple graph of order v is said to be α,β destructible if α,β are integral factors of v and an α-set of edges, E', exists whose removal from G isolates exactly the vertices in a β-set V'. Graphs which are not α, β destructible for any α.β are called stable. In this paper we prove that all graphs on a non-prime number v of vertices are α,β destructible for some a which divides v.

ISSN:1607-3606    

DOI:10.1080/16073606.1985.9631925

出版商:Taylor & Francis Group    

年代:1985

数据来源: Taylor

摘要:

In this article we apply the geometric quantization method of Rund to the case of the three-dimensional harmonic oscillator and show that the eigenvalue spectrum thus obtained coincides precisely with the energy eigenvalue spectrum that is prescribed by standard quantum mechanics.

ISSN:1607-3606    

DOI:10.1080/16073606.1985.9631926

出版商:Taylor & Francis Group    

年代:1985

数据来源: Taylor

摘要:

It is shown that the theory presented in the paper cited in the title can be extended almost effortlessly to encompass a class of gauge transformations that is considerably more general than that treated originally.

ISSN:1607-3606    

DOI:10.1080/16073606.1985.9631927

出版商:Taylor & Francis Group    

年代:1985

数据来源: Taylor

ISSN:1607-3606    

DOI:10.1080/16073606.1985.9631928

出版商:Taylor & Francis Group    

年代:1985

数据来源: Taylor