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Analytic functions of topological proper contractions

โœ Scribed by Mau-Hsiang Shih; Kok-Keong Tan


Publisher
Springer-Verlag
Year
1984
Tongue
French
Weight
303 KB
Volume
187
Category
Article
ISSN
0025-5874

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Inner functions of numerical contraction
โœ Hwa-Long Gau; Pei Yuan Wu ๐Ÿ“‚ Article ๐Ÿ“… 2009 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 146 KB

We prove that, for a function f in H โˆž of the unit disc with f โˆž 1, the existence of an operator T on a complex Hilbert space H with its numerical radius at most one and with f (T )x = 2 for some unit vector x in H is equivalent to that f be an inner function with f (0) = 0. This confirms a conjectu