Titlebook: Counterexamples in Operator Theory; Mohammed Hichem Mortad Textbook 2022 The Editor(s) (if applicable) and The Author(s), under exclusive

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Einleitung: Bedeutungen erfahrenLet . be a .-Hilbert space, and let . ∈ .(.).

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Das Normative der Kommunikationsfreiheit,Let . ∈ .(.). We say that . ∈ .(.) is a square root of . if .. = ..

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Zur Systemhaftigkeit des Rundfunks,It is well known that if ., then . denotes the modulus of .. It is possible to extend this definition to the case of linear operators.

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Wege zur Theorie des RundfunkwandelsLet . ∈ .(.) where . is a complex Hilbert space. The set . is called the spectrum of ..

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Unternehmen in der Akzeptanzkrise,Let . be in .(.). The spectral radius of . is defined as

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Problemstellung und Aufbau der Arbeit,The functional calculus aims to define .(.) where . is a fixed operator, and . belongs to some classes of functions defined in domains containing .(.), say. We already know that this is possible for any polynomial .. We also know how to define the exponential of . at an undergraduate level (this will be recalled in Chap. .).