The Cesaro Operator in ℓ² is Essentially Normal

2023/11/26 by Gül, Uğur
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2311.15245

Abstract

In this paper we prove that the Cesaro operator C in ℓ², the Hilbert space of square summable sequences, is essentially normal, i.e. the commutator [C^∗,C]:=C^∗C-CC^∗ is a compact operator on ℓ².

Related

• The Cesaro operator
• Norm of the Cesàro operator between some spaces of analytic functions
• Invariant subspaces of the Cesaro operator
• The Cesàro operator on duals of power series spaces of infinite type
• The degree of ill-posedness for some composition governed by the Cesaro operator