Automatic continuity of M-norms on C-algebras

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• 作者：Timur Oikhberg^a ; ^b ; ^{toikhber@math.uci.edu"" rel=""nofollow} ; Antonio M. Peralta^c ; ^{aperalta@ugr.es"" rel=""nofollow} ; Maribel Ram&#xed ; rez^d ; ^{mramirez@ual.es"" rel=""nofollow}
• 关键词： ; none ; color ; black"" href=""/science?_ob=MathURL&_method=retrieve&_udi=B6WK2-52HJP65-4&_mathId=mml12&_pii=S0022247X11003179&_rdoc=33&_issn=0022247X&_acct=C000029478&_version=1&_userid=578664&md5=10a340080c1cd8c4e
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2011
• 出版时间：15 September 2011
• 年：2011
• 卷：381
• 期：2
• 页码：799-811
• 全文大小：249 K

文摘

Elements a and b of a C-algebra are called orthogonal (ab) if ab=ab=0. We say that vectors x and y in a Banach space X are semi-M-orthogonal (x_SMy) if x±ymax{x,y}. We prove that every linear bijection T:A→X, where X is a Banach space, A is either a von Neumann algebra or a compact C-algebra, and T(a)_SMT(b) whenever ab, must be continuous. Consequently, every complete (semi-)M-norm on a von Neumann algebra or on a compact C-algebra is automatically continuous.