A note about Volterra operator

Abstract

Let V denote the classical Volterra operator on L2[0,1] and let z1,z2 be arbitrary complex numbers. We investigated the operator norm of $ z_{1}V+z_{2}V^{*} $.

Volterra operator norms : a brief survey

“…Finally in this section, we mention that Khadkhuu and Tsedenbayar have computed ∥αV +βV * ∥ for α, β ∈ C. For the details, we refer to [11].…”

note on self-commutators of Volterra operator and its square

“…Various results of operator norm, the numerical range for Volterra pencils have been presented in e.g. [4], [5], [6], [7] and [8].…”

Volterra-Choquet nonlinear operators

“…Compactness and cyclicity properties were studied in, e.g., [31], [20], [27], [28]. Very recent papers on various other aspects of the Volterrs operator are, e.g., [29], [24], [2], [12], [26], to mention only a few. Note that there is also a huge literature dealing with the Volterra operator in complex setting, but this aspect is out of the discussions in the present paper.…”