Article
Ufa Mathematical Journal
Volume 5, Number 1, pp. 112-124
On growth characteristics of operator-valued functions
Mishin S.N.
DOI:10.13108/2013-5-1-112
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In the work we generalize Liouville theorem and the concept of order and type of entire function to the case of an operator-valued function with values in the space ${\rm Lec}({\bf H}_1,{\bf H})$ of all linear continuous operators acting from a locally convex space ${\bf H}_1$ to a locally convex space ${\bf H}$ with an equicontinuous bornology. We find the formulae expressing the order and type of an operator-valued function in terms of the characteristics for the sequence of the coefficients. Some properties of the order and type of an operator-valued function are established.