Abstract. Let Fn, n > 2, be the free group on n generators, denoted by U1,U2, . . . ,Un. Let C¤(Fn) be the full C¤-algebra of Fn. Let X be the vector subspace of the algebraic tensor product C(Fn) C¤(Fn), spannedby 1 1,U1 1, . . . ,Un 1, 1 U1, . . . , 1 Un. Let k · kmin and k · kmax be the minimal and maximal C¤ tensor norms on C¤(Fn)C¤(Fn), and use the same notation for the corresponding (matrix) norms induced on Mk(C)X, k 2 N. Identifying X with the subspace of C¤(F2n) obtained by mapping U1 1, . . . , 1Un into the 2n generators and the identity into the identity, we get a matrix norm k · kC¤(F2n) which dominates the k · kmax norm on Mk(C)X. In this paper we prove that, with N = 2n + 1 = dimX, we have kXkmax 6 kXkC¤(F2n) 6 (N2 − N)1/2kXkmin, X 2 Mk(C) X
Radulescu, F. (2004). A comparison between the max and min norms on C∗(Fn)⊗C∗(Fn). JOURNAL OF OPERATOR THEORY, 51(2), 245-253.
A comparison between the max and min norms on C∗(Fn)⊗C∗(Fn).
RADULESCU, FLORIN
2004-10-01
Abstract
Abstract. Let Fn, n > 2, be the free group on n generators, denoted by U1,U2, . . . ,Un. Let C¤(Fn) be the full C¤-algebra of Fn. Let X be the vector subspace of the algebraic tensor product C(Fn) C¤(Fn), spannedby 1 1,U1 1, . . . ,Un 1, 1 U1, . . . , 1 Un. Let k · kmin and k · kmax be the minimal and maximal C¤ tensor norms on C¤(Fn)C¤(Fn), and use the same notation for the corresponding (matrix) norms induced on Mk(C)X, k 2 N. Identifying X with the subspace of C¤(F2n) obtained by mapping U1 1, . . . , 1Un into the 2n generators and the identity into the identity, we get a matrix norm k · kC¤(F2n) which dominates the k · kmax norm on Mk(C)X. In this paper we prove that, with N = 2n + 1 = dimX, we have kXkmax 6 kXkC¤(F2n) 6 (N2 − N)1/2kXkmin, X 2 Mk(C) XFile | Dimensione | Formato | |
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