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(d) Show that T is bounded and find ||T||. (e) Find the adjoint T* of T.

(d) Show that T is bounded and find ||T||. (e) Find the adjoint T* of T.

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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1.* Let H be a separable Hilbert space, and (en) C H a total orthonormal sequence in H. Let T: H → H be the right shift operator, defined as Tx = >(x, en-1)en for every x = :>(x, en)en- n=2 n=1 Note that, in particular, we have Ten = en+1» for every n E N.
Transcribed Image Text:1.* Let H be a separable Hilbert space, and (en) C H a total orthonormal sequence in H. Let T: H → H be the right shift operator, defined as Tx = >(x, en-1)en for every x = :>(x, en)en- n=2 n=1 Note that, in particular, we have Ten = en+1» for every n E N.
(d) Show that T is bounded and find ||T||. (e) Find the adjoint T* of T.
Transcribed Image Text:(d) Show that T is bounded and find ||T||. (e) Find the adjoint T* of T.
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