A. Defant, K. Floret, Tensor Norms and Operator Ideals,North Holland Math. Stu dies 176, 1993. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
On ideals of n-homogeneous polynomials on Banach spaces - Klaus Floret Dedicated Self-citation (Floret Ideals) (Correct)
....a) c) Sinceu ltrastability implies maximality and hence completeness, it is enou gh to showu ltrastability: For this take anu ltrafilter U r E # ) with P rq # ) 1 and # : E # T # L p # ) p # ##1. L r ( # ) # ##1aswellas# ##1. It is rather easy to see (e.g. DF, p. 227] that theu ltraprodu ct of abstract L r spaces is an abstract L r space, hence F : L r ( # ) # is an abstract L r space and, therefore, by the representation theorems of Kaku tani Bohnenblu st Nakano, F = L r ( for some positive measuk if r #. It follows (lim#, #q ....
....L r # ) # = L r ) lim #,# p# and L ##T JE ##lim#, ##1 ) For r = one has toufi the bidu l, as above. 11 3.3. For n = 2, the theory of operator ideals can be applied; for example Grothendieck s inequ ality (in the form that every operator # # # # 1 is 2dominated, DF, 17.14. and Kwapien s factorization theorem give (E) 2 (E) for all spaces (see [DF, 23. and L 2q # 3 KG# 7# #. I omit the details in 4.4. a similar calcu lation will be made) Note that C K)andL# are spaces. 3.4. The case r = is well known see Kirwan Ryan ....
[Article contains additional citation context not shown here]
A. Defant, K. Floret, Tensor Norms and Operator Ideals,North Holland Math. Stu dies 176, 1993.
Ultrastability Of Ideals Of Homogeneous Polynomials And.. - Floret, Hunfeld (1998) Self-citation (Floret Ideals) (Correct)
....j (where FIN(E) denotes thes et offinite dimens4gs snite di of E) # and # are finitely generatedtensa norms of order n. There is no general reference for the theory of tens or norms of order n 2; manyres lts however, ares traightforward generalizations of the cas n = 2 which, e.g. is treated in [DF]. 1.3. In thes ames pirit the natural projective and injective # s and # s on the n ths ymmetrictens r products #s E K) P n (E # ) An s tensor norm # of order n (ors hortly s tensg norm, if n Nis clear) asar)g to each normedsrme E anorm#( E)on# E (notation: ....
....# s (b) the metric mappingproperty: T : T : E for all T ) called finitely generated if for all E and z E) inf . detaileds tudy of # s and # s can be found in [F1] the theory of s tensg (in the s irit of Grothendieck s theory of tensg norms of order 2,s ee [DF]) will be developed in a forthcomingpaper [F2] We do not need anythingfromthis general theory inthis paper. Note that for convenience the definitions allow n to be 1: in this cas e = E # E. 1.4. Let U be an ultrafilter on as et I; the ultraproduct (alon U) of a family (E# )# #I of ....
A. Defant, K. Floret, Tensor Norms and Operator Ideals, North Holland Math. Studies 176, 1993.
Online articles have much greater impact More about CiteSeer.IST Add search form to your site Submit documents Feedback
CiteSeer.IST - Copyright Penn State and NEC