Sharpened forms of a von Neumann inequality for $\rho$-contractions

Abstract

The purpose of this paper is to give some sharpened forms of the von Neumann inequality for strict ρ-contractions which were obtained in [6], [7]. Also, some sharpened forms of the Schwarz inequality for strict ρ-contractions will be given, and as applications, corresponding inequalities for strict contractions and for uniformly stable operators will be derived. In particular, we recover the results of K. Fan [12], [13] covering the strict contractions, and in the scalar context we find an improved form of the interior Schwarz inequality quoted by R. Osserman [19].

A sharpened Schwarz-Pick operatorial inequality for nilpotent operators

“…Recall that w 1 (T ) = T and w 2 (T ) is the classical numerical radius of T . In [6], G. Cassier and N. Suciu proved the following sharpened von Neumann inequality. Theorem 4.1 ([6]).…”