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2. Let H H H where H be a Hilbert space. Let A = B(H) and B be the operator defined on H by 0 iA B = -iA* 0 Prove that || A|| = ||B|| and that B is self-adjoint.

2. Let H H H where H be a Hilbert space. Let A = B(H) and B be the operator defined on H by 0 iA B = -iA* 0 Prove that || A|| = ||B|| and that B is self-adjoint.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.6: Matrices
Problem 21E: Suppose that A is an invertible matrix over and O is a zero matrix. Prove that if AX=O, then X=O.
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2. Let H = HH where H be a Hilbert space. Let A = B(H) and B be the operator defined on H by 0 B: = iA) -¿A* Prove that || A|| ||B|| and that B is self-adjoint. =
Transcribed Image Text:2. Let H = HH where H be a Hilbert space. Let A = B(H) and B be the operator defined on H by 0 B: = iA) -¿A* Prove that || A|| ||B|| and that B is self-adjoint. =
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