摘要:

Kadec and Pelczýnski have shown that every non-reflexive subspace ofL1(μ) contains a copy ofl1complemented inL1(μ). On the other hand Rosenthal investigated the structure of reflexive subspaces ofL1(μ) and proved that such sub-spaces have non-trivial type. We show the same facts to hold true for a special class of non-reflexive Orlicz spaces. In particular we show that if F is an N-function in δ2with its complement G satisfying limt→∞G(ct)/G(t)= ∞,then every non-reflexive subspace ofL*Fcontains a copy ofl1complemented inL*F.Furthermore we establish the fact that if F is an N-function in δ2with its complement G satisfying limt→∞G(ct)/G(t)= ∞, then every reflexive subspace ofL*Fhas non-trivial type.

ISSN:1607-3606    

DOI:10.1080/16073606.1998.9632037

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

Continuing our investigation in [AF] about the sequential weak-to-norm continuity of multilinear mappings and polynomials between Banach spaces, some results about the Tsirelson spaceT, its dualT1and the James space (T1)Jmodelled overT1are obtained. Our approach simplifies various known results and generalizes some of them, for example: the completed projective tensor product, all spacesPN(T′; F) ofN-homogeneous polynomials, and the space ((H(T′; F),τω) of holomorphic functions are reflexive ifFis a reflexive Banach space of some Rademacher type or cotype. Moreover, we give some more information about the propertiesPα, and rank α which were studied by Pelczynski [P] and in [AF].

ISSN:1607-3606    

DOI:10.1080/16073606.1998.9632038

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

For each ordinal α < 1 we define a Galois correspondence between the category of closure spaces (i.e. sets endowed with an extensive and monotone closure operation taking value θ at θ) and the category of α-ary mono-relational systems. These correspondences are studied.

ISSN:1607-3606    

DOI:10.1080/16073606.1998.9632039

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

A pointwise convergence theorem is proved for automorphisms with quasi-discrete spectrum.

ISSN:1607-3606    

DOI:10.1080/16073606.1998.9632040

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

In this paper, we are mainly interested in describing constructivelyu(Z(G × C2)), whereu(ZG)has been described in some way. We first consider unitary units and prove that ifu(ZG)is generated by unitary units, thenU(Z(G× C2)) is also generated by unitary units. Then we consider bicyclic units and ask the following question: IfGhas a normal complement generated by bicyclic units, doesG × C2also have a normal complement generated by bicyclic units? We give a negative answer to the above in general, showing that none of the normal complements ofD8×C2×C2is generated by bicyclic units, although a normal complement ofD8×C2is indeed generated by bicyclic units.

ISSN:1607-3606    

DOI:10.1080/16073606.1998.9632041

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

For a unital moduleVover a commutative ringR, letCdenote the collection of cyclic submodules. The ring ϵR(V;C) = {f ε EndRV|f(C) ⊆C, ∀CεR(V;C) has been the object of several recent studies in which the structure of ϵR(V;C) is related to the triple (V, R,C). Here we introduce a new ring HR(V;C) containing ϵ(V;C) and investigate its structure in terms of the parameters (V, R, C).

ISSN:1607-3606    

DOI:10.1080/16073606.1998.9632042

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

LetGbe a graph and letvbe a vertex ofG. The open neigbourhoodN(v)ofvis the set of all vertices adjacent withvinG. An open packing ofGis a set of vertices whose open neighbourhoods are pairwise disjoint. The lower open packing number ofG, denotedρ°L(G), is the minimum cardinality of a maximal open packing ofGwhile the (upper) open packing number ofG, denotedρ°(G), is the maximum cardinality among all open packings ofG. It is known (see [7]) that ifGis a connected graph of order n ≥3, thenρ°(G)≤ 2n/3 and this bound is sharp (even for trees). As a consequence of this result, we know thatρ°L(G)≤ 2n/3. In this paper, we improve this bound whenGis a tree. We show that ifGis a tree of ordernwith radius 3, thenρ°L(G)≤n/2 + 2 √n-1, and this bound is sharp, while ifGis a tree of ordernwith radius at least 4, thenρ°L(G)is bounded above by 2n/3—O√n).

ISSN:1607-3606    

DOI:10.1080/16073606.1998.9632043

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

LetXbe a Banach space. A linear subspace ofXis called an operator range if it coincides with the range of a bounded linear operator defined on some Banach space. The paper studies disjointness and inclusion properties of various types of operator ranges in a separable infinite dimensional Banach spaceX.One of the main results is the following: LetEbe a non-closed operator range inX.ThenXcontains a non-closed dense operator rangeRwith the propertiesE∩= {0}, andRis decomposable, i.e.R=M+NwhereM,Nare closed and infinite dimensional andM∩N= {0} (Theorem 6.2).

ISSN:1607-3606    

DOI:10.1080/16073606.1998.9632044

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

We show that the normed space of μ-measurable Pettis integrable functions on a probability space with values in a Banach spaceXcontains a copy of the sequence spacec0if and only ifXcontains a copy ofc0.In this case, if the probability μ has infinite range, a copy ofc0consisting of μ-measurable functions can be found, such that it is complemented in the bigger space of all weakly μ-measurable Pettis integrable functions.

ISSN:1607-3606    

DOI:10.1080/16073606.1998.9632045

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

Using a lifting of £∞(μ,X) ([5],[6]), we construct a lifting ρxof the seminormed vector space £∞(μ,X) of measurable, essentially boundedX-valued functions. We show that in a certain sense such a lifting always exists. If μ is Lebesgue measure on (0, 1) we show that ρxexists as map from £∞((O, 1),X) → £∞,((0, l),X) if and only if X is reflexive. In general the lifted function takes its values inX**. Therefore we investigate the question, when f ε £∞(μ,X) is strictly liftable in the sense that the lifted function is a map with values even inX.

ISSN:1607-3606    

DOI:10.1080/16073606.1998.9632046

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor