摘要:

Using the notion of a spectral set introduced by von-Neumann, we give some characterizations ofC+-algebras. Two conditions, each of which is necessary and sufficient for a Banach algebra to be uniform, are also obtained.

ISSN:1607-3606    

DOI:10.1080/16073606.1999.9632099

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

This paper offers a new look at such things as the fuzzy subalgebras and congruences of an algebra, the fuzzy ideals of a ring or a lattice, and similar entities, by exhibiting them as the models, in the chosen frameTof truth values, of naturally corresponding propositional theories. This provides a systematic approach to the study of the partially ordered sets formed by these various entities, and we demonstrate its usefulness by employing it to derive a number of results, some old and some new, concerning these partially ordered sets. In particular, we prove they are complete lattices, algebraic or continuous, depending on whether T is algebraic or continuous, respectively (Proposition 3); they satisfy the same lattice identities for arbitraryTthat hold in the caseT= 2 (Corollary of Proposition 4); and they are coherent frames for any coherentTwhenever this is the case forT= 2 (Proposition 6). In addition we show, generalizing a result by Makamba and Murali [10], that the familiar classical situations where the congruences of an algebra correspond to certain other entities, such as the normal subgroups of a group or the ideals of a ring, extend to the fuzzy case by proving that the corresponding propositional theories are equivalent (Proposition 2). Further, we obtain the result of Gupta and Kantroo [5] that the fuzzy radical ideals of a commutative ring with unit are the meets of fuzzy prime ideals for arbitrary continuous T in place of the unit interval, using basic facts concerning continuous frames (Proposition 7).

ISSN:1607-3606    

DOI:10.1080/16073606.1999.9632100

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

SupposeXandYare FK spaces in which ϕ the span of the coordinate vectors (en) is dense. LetL(X,Y)denote the space of all matrices of the formEi(T(ej))asTranges over all continuous linear operators fromXintoY; hereeirepresents theithcoordinate vector andEirepresents theithcoordinate functional. LetM(L(X, Y))denote the space of all matricesBsuch that(B(i,j)A(i,j))is inL(X,Y)wheneverAis inL(X,Y).In this paper we shall show how the summability properties ofXandYdetermine the extent ofM(L(X,Y))and conversely how the extent ofM(L(X,Y))determines the summability properties of bothXandY.

ISSN:1607-3606    

DOI:10.1080/16073606.1999.9632101

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

LetXandYbe normed spaces andT: D(T)⊂X→Ya linear operator. Following R.D. Neidingcr [N1] we recall the Davis, Figiel, Johnson, Pelczynski factorization ofTcorresponding to a parameter p (1 ≤ p ≤ ∞) and apply the corresponding factorization result in [N1] to unbounded thin operators. Properties equivalent to ubiquitous thinness arc derived. Defining an operatorTto be cothin if its adjoint is thin, a dual factorization result for cothin operators is obtained, where for each 1 < p < ∞, the intermediate space in the factorization is cohereditarilylp.This result is shown to hold more generally for the cases whenTis either partially continuous or closable; in particular, such operators are strictly cosingular. A condition for a closable weakly compact operator to be strictly cosingular follows as a corollary.

ISSN:1607-3606    

DOI:10.1080/16073606.1999.9632102

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

ISSN:1607-3606    

DOI:10.1080/16073606.1999.9632103

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

ISSN:1607-3606    

DOI:10.1080/16073606.1999.9632098

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor