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On a positive linear map preserving absolute values

✍ Scribed by Leroy B. Beasley; An-Hyun Kim; Woo Young Lee

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 447 KB
Volume: 260
Category: Article
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(97)80015-8

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✦ Synopsis

Suppose m is an n X 12 (n 2 2) matrix algebra over a C*-algebra g, and Q? is a C*-algebra. If p : i?X + '23 is a positive, disjoint linear map, then p preserves absolute values. In particular, for a linear map rp : '?I + '$3 of P-algebras, p preserves absolute values if and only if it is positive and "ultraweakly disjoint." 0 Elsevier Science Inc., 1997 Throughout this note, suppose %Y and ?Z? are unital C*-algebras, and suppose the set %+ = {a*a : a

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