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Let TE B(H) be an invertible self-adjoint operator. Show that ||T−¹|| = inf{|\| : λ = o(T)}¯¹

Let TE B(H) be an invertible self-adjoint operator. Show that ||T−¹|| = inf{|\| : λ = o(T)}¯¹

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Let TE B(H) be an invertible self-adjoint operator. Show that ||T-| = inf{|A| : A E O(T)}-1
Transcribed Image Text:Let TE B(H) be an invertible self-adjoint operator. Show that ||T-| = inf{|A| : A E O(T)}-1
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