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On the real and imaginary parts of powers of the Volterra operator
Thomas Ransford, Dashdondog Tsedenbayar
We study the real and imaginary parts of the powers of the Volterra operator on , specifically their eigenvalues, their norms and their numerical ranges.
Asymptotically equicontinuous sequences of operators and a Banach-Steinhaus type theorem
Javad Mashreghi, Thomas Ransford
We introduce the notion of an asymptotically equicontinuous sequence of linear operators, and use it to prove the following result. If are topological vector spaces, if $T_n,…
Summability and duality
Soumitra Ghara, Javad Mashreghi, Thomas Ransford
We formalize the observation that the same summability methods converge in a Banach space and its dual . At the same time we determine conditions under which these methods…
Norms of polynomials of the Volterra operator
Thomas Ransford, Nathan Walsh
We compute the operator norm of real-quadratic polynomials of the Volterra operator. This is used to test whether the Crouzeix conjecture holds for the Volterra operator.
The norm of the resolvent of the Volterra operator
Thomas Ransford
In this expository note, we compute the exact value of the norm of the resolvent of the Volterra operator.
Spectral sets for numerical range
Hubert Klaja, Javad Mashreghi, Thomas Ransford
We define and study a numerical-range analogue of the notion of spectral set. Among the results obtained are a positivity criterion and a dilation theorem, analogous to those alrea…