A noncompletely continuous operator on whose random Fourier transform is in
Authors:
N. Ghoussoub and M. Talagrand
Journal:
Proc. Amer. Math. Soc. 92 (1984), 229-232
MSC:
Primary 46G99; Secondary 47B38
DOI:
https://doi.org/10.1090/S0002-9939-1984-0754709-1
MathSciNet review:
754709
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: Let be a bounded linear operator from
into
, where
is a compact abelian metric group with its Haar measure, and
is a probability space. Let
be the random measure on
associated to
; that is,
for each
in
.
We show that, unlike the ideals of representable and Kalton operators, there is no subideal of
such that
is completely continuous if and only if
for almost
in
. We actually exhibit a noncompletely continuous operator
such that
for each
.
- [1] H. Chernoff, A measure of asymptotic efficiency for tests of a hypothesis based on the sum of observations, Ann. Math. Statist 23 (1952), 493-509. MR 0057518 (15:241c)
- [2]
H. Fakhoury, Représentations d'opérateurs à valeurs dans
, Math Ann. 240 (1979), 203-213. MR 526843 (80e:47027)
- [3]
N. Kalton, The endomorphisms of
, preprint, 1979.
- [4] H. P. Rosenthal, Convolution by a biased coin, The Altgeld book 1975/1976, University of Illinois Functional Analysis Seminar.
Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46G99, 47B38
Retrieve articles in all journals with MSC: 46G99, 47B38
Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1984-0754709-1
Article copyright:
© Copyright 1984
American Mathematical Society