Automatic continuity of M-norms on C*-algebras

作者：Oikhberg Timur; Peralta Antonio M^*; Ramirez Maribel

来源：Journal of Mathematical Analysis and Applications, 2011, 381(2): 799-811.

DOI：10.1016/j.jmaa.2011.03.066

• C*-algebra .
• Compact C*-algebra
• Von Neumann algebra
• Orthogonality preservers
• (Semi-)M-norm
• (Semi-)M-orthogonality

Elements a and b of a C*-algebra are called orthogonal (a perpendicular to b) if a*b = ab* = 0. We say that vectors x and y in a Banach space X are semi-M-orthogonal (x perpendicular to (SM) y) if parallel to x +/- y parallel to >= max{parallel to x parallel to, parallel to y parallel to}. 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) perpendicular to(SM) T(b) whenever a perpendicular to b, must be continuous. Consequently, every complete (semi-)M-norm on a von Neumann algebra or on a compact C*-algebra is automatically continuous.

• 出版日期2011-9-15