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Chapter 12: Similarity Condition Numbers of Unbounded Diagonalizable Operators

https://doi.org/10.1142/9789813221277_0012Cited by:0 (Source: Crossref)

Abstract:

As in the finite dimensional case an operator A in a separable Hilbert space ℋ is said to be a diagonalizable operator, if there are a boundedly invertible operator T ∈ ℬ(ℋ) and a normal operator D acting in ℋ, such that

T H x = D T x (x \in D o m (H)) . (0.1)

$T H x = D T x (x \in D o m (H)) . (0.1)$

Besides,

κ_{T} = ∥ T^{-1} ∥ ∥ T ∥ ∥

$κ_{T} = ∥ T^{-1} ∥ ∥ T ∥$ is the condition number.

In this chapter we consider some unbounded diagonalizable operators and derive bounds for the condition numbers of the considered operators. We also discuss applications of the obtained bounds to spectrum perturbations and operator functions.

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Chapter 12: Similarity Condition Numbers of Unbounded Diagonalizable Operators

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