On the transpose map of matrix algebras

Author:
Jun Tomiyama

Journal:
Proc. Amer. Math. Soc. **88** (1983), 635-638

MSC:
Primary 46L05; Secondary 16A42

MathSciNet review:
702290

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Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that for the transpose map of the matrix algebra , its th multiplicity map has exactly the norm if , hence the completely bounded norm of written equals . Some applications and related results are also proved.

**[1]**William B. Arveson,*Subalgebras of 𝐶*-algebras*, Acta Math.**123**(1969), 141–224. MR**0253059****[2]**Erik Christensen,*Extensions of derivations. II*, Math. Scand.**50**(1982), no. 1, 111–122. MR**664512****[3]**U. Haagerup,*Solution of similarity problem for cyclic representations of**-algebras*, preprint.**[4]**T. Huruya and J. Tomiyama,*Completely bounded maps of**-algebras*, J. Operator Theory (to appear).**[5]**Christopher Lance,*On nuclear 𝐶*-algebras*, J. Functional Analysis**12**(1973), 157–176. MR**0344901****[6]**Richard I. Loebl,*Contractive linear maps on 𝐶*-algebras*, Michigan Math. J.**22**(1975), no. 4, 361–366 (1976). MR**0397423****[7]**Takateru Okayasu,*Some cross norms which are not uniformly cross*, Proc. Japan Acad.**46**(1970), 54–57. MR**0264414****[8]**Toshiyuki Takasaki and Jun Tomiyama,*Stinespring type theorems for various types of completely positive maps associated to operator algebras*, Math. Japon.**27**(1982), no. 1, 129–139. MR**649029****[9]**Gerd Wittstock,*Ein operatorwertiger Hahn-Banach Satz*, J. Funct. Anal.**40**(1981), no. 2, 127–150 (German, with English summary). MR**609438**, 10.1016/0022-1236(81)90064-1

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1983-0702290-4

Keywords:
Completely bounded map,
-algebra,
matrix algebra

Article copyright:
© Copyright 1983
American Mathematical Society