Misra, Gadadhar ; Pati, Vishwambhar (1990) Contractive and completely contractive modules, matricial tangent vectors and distance decreasing metrics Journal of Operator Theory, 91 . pp. 213220. ISSN 03794024

PDF
 Author Version
225kB 
Official URL: http://www.math.iisc.ernet.in/~gm/gmhomefiles/pape...
Abstract
It is shown that a tangent vector v in T_{ω}Ω determines a finite dimensional Hilbert module over H^{∞} (Ω) and that the module is contractive if and only if C_{Ωω}(v), the Caratheodory length of v, is less or equal to one. More generally, an element V of T_{ω}Ω ⊗ M_{n} also determines a finite dimensional Hilbert module over H^{∞} (Ω) and if the norm on T_{ωΩ}⊗ M_{n} 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.
Item Type:  Article 

Source:  Copyright of this article belongs to The Theta Foundation. 
ID Code:  67122 
Deposited On:  28 Oct 2011 10:30 
Last Modified:  18 May 2016 14:22 
Repository Staff Only: item control page