Representations of completely bounded multilinear operators
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Representations of completely bounded multilinear operators. / Christensen, Erik; Sinclair, Allan M.
In: Journal of Functional Analysis, Vol. 72, No. 1, 05.1987, p. 151-181.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - Representations of completely bounded multilinear operators
AU - Christensen, Erik
AU - Sinclair, Allan M.
PY - 1987/5
Y1 - 1987/5
N2 - A definition of a completely bounded multilinear operator from one C*-algebra into another is introduced. Each completely bounded multilinear operator from a C*-algebra into the algebra of bounded linear operators on a Hilbert space is shown to be representable in terms of *-representations of the C*-algebra and interlacing operators. This result extends Wittstock's Theorem that decomposes a completely bounded linear operator from a C*-algebra into an injective C*-algebra into completely positive linear operators.
AB - A definition of a completely bounded multilinear operator from one C*-algebra into another is introduced. Each completely bounded multilinear operator from a C*-algebra into the algebra of bounded linear operators on a Hilbert space is shown to be representable in terms of *-representations of the C*-algebra and interlacing operators. This result extends Wittstock's Theorem that decomposes a completely bounded linear operator from a C*-algebra into an injective C*-algebra into completely positive linear operators.
UR - http://www.scopus.com/inward/record.url?scp=0000692027&partnerID=8YFLogxK
U2 - 10.1016/0022-1236(87)90084-X
DO - 10.1016/0022-1236(87)90084-X
M3 - Journal article
AN - SCOPUS:0000692027
VL - 72
SP - 151
EP - 181
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
SN - 0022-1236
IS - 1
ER -
ID: 384124094