Idempotent, model, and Toeplitz operators attaining their norms

The norm attainment problem for functions of projections

“…Applying Lemma 2 to A * A and taking into account that trace Φ A * A = φ and det Φ A * A = |ω| 2 , we see that the eigenvalues λ of A * A are characterized by the property that the spectral measure of the set {x ∈ σ(H):…”

“…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.…”

“…Proof. It is clear that T ∈ N : the norm is attained at the vector (1/ 1 + ω 2 1 , −ω 1 / 1 + ω 2 1 , 0, 0, . .…”

Norms of basic operators in vector valued model spaces and de Branges spaces

“…It is easy to see that the compact operators are norm attaining. Some additional classes of operators that attain their norm are considered in [3,4,6,7,13].…”

“…In [3, Proposition 3.1] it was shown that when Ω + = D, then A 0 ∈ N A and A 0 = 1 if and only if there exists a nonzero vector f ∈ H(Θ) with f (0) = 0 for Hilbert space valued Hardy spaces. The norm of A 0 was then evaluated when m = 1; see [3,Theorem 3.3] and [10, Section 7, Corollary 3].…”