Let TE B(H) be a self-adjoint operator on a Hilbert space H (a) Use the continuous functional calculus to show that T20 if o(T) C [0, ∞). (b) Show that T is an orthogonal projection if and only if (T) C {0, 1}.
Let TE B(H) be a self-adjoint operator on a Hilbert space H (a) Use the continuous functional calculus to show that T20 if o(T) C [0, ∞). (b) Show that T is an orthogonal projection if and only if (T) C {0, 1}.
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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Transcribed Image Text:2. Let T = B(H) be a self-adjoint operator on a Hilbert space H
(a) Use the continuous functional calculus to show that T20 if o(T) [0, ∞).
(b) Show that T is an orthogonal projection if and only if (T) C {0, 1}.
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