Idempotent, model, and Toeplitz operators attaining their norms

2021/01/10 by Bala, Neeru, Dhara, Kousik, Sarkar, Jaydeb +1 · 2 citations
#30J05 #47A10 #47A46 #47B07 #47B35 #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2101.03585

Abstract

We study idempotent, model, and Toeplitz operators that attain the norm. Notably, we prove that if Q is a backward shift invariant subspace of the Hardy space H²(\mathbbD), then the model operator S_Q attains its norm. Here S_Q = P_QM_z|_Q, the compression of the shift M_z on the Hardy space H²(\mathbbD) to Q.

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