Contractive and completely contractive modules, matricial tangent vectors and distance decreasing metrics

Misra, Gadadhar ; Pati, Vishwambhar (1990) Contractive and completely contractive modules, matricial tangent vectors and distance decreasing metrics Journal of Operator Theory, 91 . pp. 213-220. ISSN 0379-4024

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Abstract

It is shown that a tangent vector v in TωΩ determines a finite dimensional Hilbert module over H (Ω) and that the module is contractive if and only if CΩω(v), the Caratheodory length of v, is less or equal to one. More generally, an element V of TωΩ ⊗ Mn also determines a finite dimensional Hilbert module over H (Ω) and if the norm on TωΩ⊗ Mn is understood to be the injective tensor product norm then again the module is contractive if and only if ||V|| is less or equal to one. The question of which contractive modules are completely contractive over H (Ω) is discussed in terms of the Caratheodory metric on Ω. The relationship of this question with certian aspects of the theory of tensor products for operator spaces is established.

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Deposited On:28 Oct 2011 10:30
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