Idempotent, model, and Toeplitz operators attaining their norms

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 H 2 (D), then the model operator S Q attains its norm. Here S Q = P Q M z | Q , the compression of the shift M z on the Hardy space H 2 (D) to Q.

The norm attainment problem for functions of projections

“…From ( 2) and (3) and the equalities M 00 = M 11 = 0 we infer that We conclude with some examples. The authors of [2] recently proved that a skew projection T is in N if and only if the selfadjoint operator T + T * − I belongs to N . The operator T + T * − I appeared in [5] and is therefore called the Buckholtz operator in [2].…”

“…The authors of [2] recently proved that a skew projection T is in N if and only if the selfadjoint operator T + T * − I belongs to N . The operator T + T * − I appeared in [5] and is therefore called the Buckholtz operator in [2]. The following is an extension of this result.…”