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Uncorrelatedness and orthogonality for vector-valued processes
Author(s):
Peter
A.
Loeb;
Horst
Osswald;
Yeneng
Sun;
Zhixiang
Zhang
Journal:
Trans. Amer. Math. Soc.
356
(2004),
3209-3225.
MSC (2000):
Primary 03H05, 28E05, 47H60;
Secondary 26E35
Posted:
November 25, 2003
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Abstract:
For a square integrable vector-valued process  on the Loeb product space, it is shown that vector orthogonality is almost equivalent to componentwise scalar orthogonality. Various characterizations of almost sure uncorrelatedness for  are presented. The process  is also related to multilinear forms on the target Hilbert space. Finally, a general structure result for  involving the biorthogonal representation for the conditional expectation of  with respect to the usual product  -algebra is presented.
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Additional Information:
Peter
A.
Loeb
Affiliation:
Department of Mathematics, University of Illinois, 1409 West Green St., Urbana, Illinois 61801
Email:
loeb@math.uiuc.edu
Horst
Osswald
Affiliation:
Mathematisches Institut der LMU-München, Theresienstr.39, D-80333 München, Germany
Email:
Horst.Osswald@mathematik.uni-muenchen.de
Yeneng
Sun
Affiliation:
Institute for Mathematical Sciences, National University of Singapore, 3 Prince George's Park, Singapore 118402, Republic of Singapore, -- and -- Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore 117543, Republic of Singapore
Email:
matsuny@nus.edu.sg
Zhixiang
Zhang
Affiliation:
Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore 117543, Republic of Singapore, -- and -- School of Mathematical Sciences, Peking University, Beijing 100871, People's Republic of China
Email:
matzzx@nus.edu.sg
DOI:
10.1090/S0002-9947-03-03450-0
PII:
S 0002-9947(03)03450-0
Keywords:
Vector-valued processes,
Loeb product space,
Keisler's Fubini Theorem,
orthogonality,
uncorrelatedness,
multilinear functional
Received by editor(s):
March 11, 2003
Posted:
November 25, 2003
Additional Notes:
The authors are grateful for the support of the National University of Singapore during the initiation of this work
Copyright of article:
Copyright
2003,
American Mathematical Society
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