naa a22 4500 510760708 CHVBK 20180411083138.0 cr unu---uuuuu 180411e20130101xx s 000 0 eng 10.1007/s13163-011-0089-0 doi (NATIONALLICENCE)springer-10.1007/s13163-011-0089-0 Automatic continuity of orthogonality or disjointness preserving bijections [Elektronische Daten] [Timur Oikhberg, Antonio Peralta, Daniele Puglisi] Elements a and b of a non-commutative L p (M,τ) space associated to a von Neumann algebra, M, equipped with a normal semi-finite faithful trace τ, are called orthogonal if l(a)l(b)=r(a)r(b)=0, where l(x) and r(x) denote the left and right support projections of x. A linear map T from L p (M,τ) to a normed space X is said to be orthogonality-to-p-orthogonality preserving if ∥T(a)+T(b)∥ p =∥a∥ p +∥b∥ p whenever a and b are orthogonal. In this paper, we prove that an orthogonality-to-p-orthogonality preserving linear bijection from L p (M,τ) to a Banach space is automatically continuous if 1≤p<∞, and M is either an abelian von Neumann algebra or a discrete von Neumann algebras. Furthermore, any complete p-additive norm on such L p (M,τ) is equivalent to the canonical norm. Revista Matemática Complutense, 2011 Non-commutative L p spaces nationallicence Banach lattices nationallicence Von Neumann algebras nationallicence Orthogonality preservers nationallicence p -orthogonality nationallicence Oikhberg Timur Dept. of Mathematics, University of California-Irvine, 92697, Irvine, CA, USA aut Peralta Antonio Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071, Granada, Spain aut Puglisi Daniele Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071, Granada, Spain aut Revista Matemática Complutense Springer Milan 26/1(2013-01-01), 57-88 1139-1138 26:1<57 2013 26 13163 https://doi.org/10.1007/s13163-011-0089-0 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s13163-011-0089-0 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Oikhberg Timur Dept. of Mathematics, University of California-Irvine, 92697, Irvine, CA, USA aut NATIONALLICENCE 700 1- Peralta Antonio Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071, Granada, Spain aut NATIONALLICENCE 700 1- Puglisi Daniele Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071, Granada, Spain aut NATIONALLICENCE 773 0- Revista Matemática Complutense Springer Milan 26/1(2013-01-01), 57-88 1139-1138 26:1<57 2013 26 13163 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer