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γ-Radonifying operators and entropy ideals

✍ Scribed by Thomas Kühn

Publisher
John Wiley and Sons
Year
1982
Tongue
English
Weight
300 KB
Volume
107
Category
Article
ISSN
0025-584X

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✦ Synopsis

0. htroductio11

I i i 1967 R. 31. DIDLEY [4] introduced the notion of so-called CrC-set.s. These are sul)sets of a HILRERY space on which the canonical linear GAtrssian process on This HII~HERT space has a sample-coiitin~ious version. DVULEY fotiiicl a sufficient c.ondition for a set to l)e a GC-set in terms of its e-entropy. -4 siniilnr necessary ioiitlitioii wai; given hy V. N. SCJ)AKOI-[It:] i n 1971. (poi: different proofs see also A Y~r.:.rsc:rr defined in his monogra1)h [lo] entropy numhers of opemtors wtiiig l~t.t\reeii KAS'ACH spaces. So the concept of eiitro1)y was carried over from sets t o cqierrttors. On the other hand the 1)roperties of GC-sets can I)e expressed in thc Iitiigiatge of operators. too. namely with the help of yR,ADOsifying operators.

Tlic aim of this note is to "translate" the results of DCr>r,T;;. And SUI)BKOV ineiitioned sl)ow into the "operator language" and to prove them i i i an adequate x i y . l'herehy ideas of [4] and [3] are used. Moreover it is shown how these results c . a i t I)c iiii~~roved iii KANACH spaces of type itnrl cotype 2. Filially some examples are ,given and two problems are stated.

; 1 . Exp. 1'1111 und [12]).

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