Completely bounded modules and associated extremal problems

Misra, Gadadhar ; Narasimha Sastry, N. S. (1990) Completely bounded modules and associated extremal problems Journal of Functional Analysis, 91 (2). pp. 213-220. ISSN 0022-1236

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In this paper we continue our study of certain finite dimensional Hilbert modules over the function algebra A (Ω), Ω ⊆ Cm. We show that these modules are always completely bounded with the bound obtained as the matrix valued analogue of a certain scalar valued extremal problem. In particular, we obtain a necessary and sufficient condition for our module to be completely contractive. We produce a contractive module CNm over A (Bm) such that it is completely bounded with the complete bound equal to √m; that is, CNm is not completely contractive.

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