The ell-p norm of C-I, where C is the Cesaro operator

Jameson, Graham (2021) The ell-p norm of C-I, where C is the Cesaro operator. Mathematical Inequalities and Applications, 24 (2). pp. 551-557. ISSN 1331-4343

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Abstract

For the Cesaro operator C, it is known that ||C-I||_2 = 1. Here we prove that ||C-I||_4 < 3^(1/4) and ||C^T-I||_4 = 3. Bounds for intermediate values of p are derived from the Riesz-Thorin interpolation theorem. An estimate for lower bounds is obtained.