The direct product of R infinity many times with itself is denoted by R. It is the
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Question:
The direct product of R infinity many times with itself is
denoted by R∞. It is the set of all infinite tuples of elements of R and it
is a vectors space over R. Given a vector x = (x1, x2, . . . ) ∈ R∞ mapping
x to the vector (x2, x3, . . . ) would form a linear map from R∞ to R∞.
Such a map is called backward shift.
i. Is backward shift injective? Justify your answer.
ii. Define a T ∈ L(R∞, R∞) which is not a backward shift but it is injective.
Related Book For
International Marketing And Export Management
ISBN: 9781292016924
8th Edition
Authors: Gerald Albaum , Alexander Josiassen , Edwin Duerr
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