Geodesic
On growth characteristics of operator-valued functions
Ufa mathematical journal, Tome 5 (2013) no. 1, pp. 112-124 Cet article a éte moissonné depuis la source Math-Net.Ru

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In the work Liouville theorem and the concept of order and type of entire function are generalized to the case of operator-valued function with values in the space $\mathrm{Lec}(\mathbf{H}_1,\mathbf{H})$ of all linear continuous operators acting from a locally convex space $\mathbf{H}_1$ to a locally convex space $\mathbf{H}$ with equicontinuous bornology. We find the formulae expressing the order and type of operator-valued function in terms of characteristics of the sequence of coefficients. Some properties of order and type of operator-valued function are established.
Keywords: locally convex space, order and type of sequence of operators, order and type of entire function, equicontinuous bornology, convergence by bornology, operator-valued function. 
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S. N. Mishin. On growth characteristics of operator-valued functions. Ufa mathematical journal, Tome 5 (2013) no. 1, pp. 112-124. http://geodesic.mathdoc.fr/item/UFA_2013_5_1_a9/

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