ABSTRACT
Bounded operators on a Hilbert space https://www.w3.org/1998/Math/MathML"> H → https://s3-euw1-ap-pe-df-pch-content-public-u.s3.eu-west-1.amazonaws.com/9780203702413/25d3d2fa-ace6-48b7-8621-e244393a3acf/content/eq3665.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> have many of the properties of operators defined on https://www.w3.org/1998/Math/MathML"> V → N https://s3-euw1-ap-pe-df-pch-content-public-u.s3.eu-west-1.amazonaws.com/9780203702413/25d3d2fa-ace6-48b7-8621-e244393a3acf/content/eq3666.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> . For example, Theorem 13.1(1) and Corollary 13.1(1) apply, e.g., for bounded operators we have () https://www.w3.org/1998/Math/MathML"> 〈 ϕ → | A ^ ϕ → 〉 = 〈 ϕ → | B ^ ϕ → 〉 ∀ ϕ → ∈ H → ⇒ A ^ = B ^ . https://s3-euw1-ap-pe-df-pch-content-public-u.s3.eu-west-1.amazonaws.com/9780203702413/25d3d2fa-ace6-48b7-8621-e244393a3acf/content/eq3667.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/>
