摘要:

Answering a question posed by J. Diestel we construct for every infinite-dimensional Banach spaceXanX-valued Pettis integrable functionfon [0,1] for whichF(t) = ∫t0f(x)dxis non-differentiable on a set of positive measure.

ISSN:1607-3606    

DOI:10.1080/16073606.1994.9631753

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

Results are derived concerning the spectral properties of an elliptic boundary value problem arising in the mathematical theory of magnetohydrodynamics which are of basic importance for the further development of this theory.

ISSN:1607-3606    

DOI:10.1080/16073606.1994.9631754

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

On suitable Banach spaces, the existence of a certain functional calculus for an operator is equivalent to that operator having a certain integral repreaentation with respect to some family of projections. In this paper we consider the problem of identifying the precise classes of spaces on which these equivalences hold, for several of the most important functional calculi.

ISSN:1607-3606    

DOI:10.1080/16073606.1994.9631755

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

A ringRis called pseudo-commutative if for eachx,yεRthere exists an integer n = n(x, y) for whichxy = nyx.We first show that a generalization of a commutativity condition of Chacron and Thierrin implies pseudo-commutativity in rings; we then study pseudo-commutativity and commutativity in rings with constraints of the formxy =σkiyixi, where the kiare integers.

ISSN:1607-3606    

DOI:10.1080/16073606.1994.9631756

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

We give a short proof of the Riddle-Saab-Uhl theorem on Pettis integrability in dual Banach spaces, avoiding the use of Banach space techniques and extending it to certain locally convex spaces.

ISSN:1607-3606    

DOI:10.1080/16073606.1994.9631757

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

Certain topological countability properties are generalized to interior algebras and basic reaults concerning these properies are investigated. The preservation of these properties under the formation of principal quotients and under a new construction called ajoinof interior algebras, is investigated.

ISSN:1607-3606    

DOI:10.1080/16073606.1994.9631758

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

The classes of strongly prime, uniformly strongly prime and superprime hemirings are defined and shown to be special classes. Intersection properties of the radicals generated by these classes are studied and related to α-ideas. Hemiring radicals and ring radicals of rings are shown to be identical for these three radical concepts.

ISSN:1607-3606    

DOI:10.1080/16073606.1994.9631759

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

IfYis a closed, finite-codimensional subspace ofl1the extreme points of the closed unit ballBYhave finite support. This is used to show that every member ofBYis expressible as an infinite convex series of extreme points ofBY.

ISSN:1607-3606    

DOI:10.1080/16073606.1994.9631760

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

The properties of the factorization system corresponding to an open localization of a finitely complete and finitely cocomplete category are described.

ISSN:1607-3606    

DOI:10.1080/16073606.1994.9631761

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

The classical theorem of Dunford and Pettis identifies the bounded, uniformly integrable subsets of L1(μ) with the relatively weakly compact sets. Another characterization of uniform integrability is given in a theorem of De La Vallée Poussin which states that asubset K of L1(μ) is bounded and uniformly integrable if and only if there is an N-function F so thatsup{f F(f)dμ: f ε K} < ∞. De La Vallée Poussin's theorem is the focal point of the fmt part of this paper as well as the driving force for the results in the second part. We refine and improve this theorem in several directions. The theorem of De La Vallée Poussin does not, for instance, specify just how well the functionFcan be chosen. It gives little additional information in case the set in question is relatively norm compact inL1(μ).Finally it gives no information on the structure of the set in the corresponding Band space of F-integrable functions. More specifically we establish the fact that asubset K of L1is relatively compact if and only if there is an N-function Fε δ'so that K is relatively compact in L*F.Furthermore we prove thata subset K of L1is relatively weakly compact if and only if there is an N-function Fε δ'so that K is relatively weakly compact in L*F.We then go on to show that a large class of non-reflexive Orlicz spaces has the weak Band-Saks property, by establishing a result for these spaces, very similar to the Dunford-Pettis theorem forL1.

ISSN:1607-3606    

DOI:10.1080/16073606.1994.9631762

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor