caa a22 4500 388046457 CHVBK 20180307125039.0 cr unu---uuuuu 161130e199812 xx s 000 0 eng 10.1017/S1446788700035953 doi S1446788700035953 pii (NATIONALLICENCE)cambridge-10.1017/S1446788700035953 Randrianantoanina Narcisse Department of Mathematics and Statistics, Miami University, Oxford, OH 45056 e-mail: randrin@muohio.edu Hilbert transform associated with finite maximal subdiagonal algebras [Elektronische Daten] [Narcisse Randrianantoanina] Let be a von Neumann algebra with a faithful normal trace τ, and let H∞ be a finite, maximal. subdiagonal algebra of . We prove that the Hilbert transform associated with H∞ is a linear continuous map from L1 (, τ) into L1.∞ (, τ). This provides a non-commutative version of a classical theorem of Kolmogorov on weak type boundedness of the Hilbert transform. We also show that if a positive measurable operator b is such that b log+ b L1 (, τ) then its conjugate b, relative to H∞ belongs to L1 (, τ). These results generalize classical facts from function algebra theory to a non-commutative setting. Copyright © Australian Mathematical Society 1998 46L50 nationallicence 46E15 nationallicence secondary 43A15 nationallicence 47D15 nationallicence von-Neumann algebras nationallicence conjugate functions nationallicence Hardy spaces nationallicence Journal of the Australian Mathematical Society Cambridge University Press 65/3(1998-12), 388-404 1446-7887 65:3<388 1998 65 JAZ https://doi.org/10.1017/S1446788700035953 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S1446788700035953 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Randrianantoanina Narcisse Department of Mathematics and Statistics, Miami University, Oxford, OH 45056 e-mail: randrin@muohio.edu NATIONALLICENCE 773 0- Journal of the Australian Mathematical Society Cambridge University Press 65/3(1998-12), 388-404 1446-7887 65:3<388 1998 65 JAZ CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge