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2. Let (ei)ier and (fi) jer be the orthonormal bases for the Hilbert spaces X and Y respec- tively. If for each i Є I, set T(ei) = fi, show that T can be extended to a unitary operator from X onto Y.

2. Let (ei)ier and (fi) jer be the orthonormal bases for the Hilbert spaces X and Y respec- tively. If for each i Є I, set T(ei) = fi, show that T can be extended to a unitary operator from X onto Y.

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.CR: Review Exercises
Problem 47CR: Find an orthonormal basis for the subspace of Euclidean 3 space below. W={(x1,x2,x3):x1+x2+x3=0}
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2. Let (ei)ier and (fi) jer be the orthonormal bases for the Hilbert spaces X and Y respec- tively. If for each i Є I, set T(ei) = fi, show that T can be extended to a unitary operator from X onto Y.
Transcribed Image Text:2. Let (ei)ier and (fi) jer be the orthonormal bases for the Hilbert spaces X and Y respec- tively. If for each i Є I, set T(ei) = fi, show that T can be extended to a unitary operator from X onto Y.
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