2001, Volume 4, Number 4, pp.318-321
The formula for the spectral radius of arbitrary
weighted shift operators acting in Lp spaces is established.
The formula contains as a component a new dynamical invariant - T-entropy
(a mathematical analogue to the thermodynamic entropy). It
is proved that the logarithm of the spectral radius
and the T-entropy are linked by the Legendre transform.
Key words: T-entropy, weighted shift operator, Legendre transform, spectral radius
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