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oai:www.ideals.illinois.edu:2142/86802 2023-07-11 col_2142_5131 col_2142_16340 com_2142_5130 com_2142_16339 com_2142_8903

Burkholder, Donald L. Junge, Marius Musat, Magdalena Elena 2015-09-28T15:19:36Z 2015-09-28T15:19:36Z 10000-01-01 2002 2002 We prove that for 1 &le; p < q < infinity the analogue of the classical result BMO,Lp pq = Lq holds in the setting of a finite von Neumann algebra M , equipped with an increasing filtration ( M n)n&ge;1 of von Neumann subalgebras. We also obtain the corresponding results for the real method of interpolation. We discuss the appropriate operator space matrix norms and show that these interpolation results hold in the category of operator spaces. We apply further interpolation techniques to the study of the operator space UMD property, introduced by Pisier in the context of non-commutative vector-valued Lp-spaces, associated to a hyperfinite (and finite) von Neumann algebra. We discuss basic stability properties of UMDp operator spaces. It is unknown whether the property is independent of p in this setting. We show that for 1 < p, q < infinity, the Schatten q-classes Sq are UMDp. We provide further examples of UMDp (independent of p) operator spaces, including the non-commutative Lorentz spaces associated to a hyperfinite (and finite) von Neumann algebra. Made available in DSpace on 2015-09-28T15:19:36Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 3070392.pdf: 4258338 bytes, checksum: 047f83824148300a5506a43128c9f91c (MD5) Previous issue date: 2002 Embargo set by: Seth Robbins for item 88083 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs U of I Only 119 p. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2002. http://hdl.handle.net/2142/86802 (MiAaPQ)AAI3070392 eng Mathematics On the Operator Space UMD Property and Non-Commutative Martingale Inequalities text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.