TENSOR EXTENSION PROPERTIES OF C(K)-REPRESENTATIONS AND APPLICATIONS TO UNCONDITIONALITY

Journal of the Australian Mathematical Society

CHRISTOPH KRIEGLER¹ 

[1] CHRISTIAN LE MERDY

关键词: primary 47A60;    secondary 46B28;   

DOI  :  10.1017/S1446788709000433

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

Let K be any compact set. The C*-algebra C(K) is nuclear and any bounded homomorphism from C(K) into B(H), the algebra of all bounded operators on some Hilbert space H, is automatically completely bounded. We prove extensions of these results to the Banach space setting, using the key concept ofR-boundedness. Then we apply these results to operators with a uniformly bounded H∞-calculus, as well as to unconditionality on Lp. We show that any unconditional basis on Lp ‘is’ an unconditional basis on L2 after an appropriate change of density.

【 授权许可】

Unknown