Norms on super-reflexive Banach spaces
Renorming Banach spaces with many projections and smoothness properties.
Basic sequences and smooth norms in Banach spaces
Numerical ranges of some composition operators.
This paper is a short survey on the numerical range of some composition operators. The first part is devoted to composition operators on the Hilbert Hardy space H2 on the unit disk. The results are due to P. Bourdon, J. Shapiro and V. Matache.
In the second part we study the numerical range of composition operators on the Hilbert space
An extension of Simons' inequality and applications.
This article is devoted to an extension of Simons' inequality. As a consequence, having a pointwise converging sequence of functions, we get criteria of uniform convergence of an associated sequence of functions.
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