Geodesic
The numerical radius of a weighted shift operator with geometric weights
The electronic journal of linear algebra, Tome 18 (2009), pp. 58-63.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Let T be a weighted shift operator T on the Hilbert space 2 (N) with geometric weights. Then the numerical range of T is a closed disk about the origin, and its numerical radius is determined in terms of the reciprocal of the minimum positive root of a hypergeometric function. This function is related to two Rogers-Ramanujan identities.
Classification : 47A12, 47B37, 33D15
Keywords: numerical radius, weighted shift operator, Rogers-Ramanujan identities 
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     title = {The numerical radius of a weighted shift operator with geometric weights},
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Chien, Mao-Ting; Nakazato, Hiroshi. The numerical radius of a weighted shift operator with geometric weights. The electronic journal of linear algebra, Tome 18 (2009), pp. 58-63. http://geodesic.mathdoc.fr/item/ELA_2009__18__a53/