عنوان مجله
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JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
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چکیده
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In this manuscript, we present several new results in finite and countable dimen-
sional real Hilbert space norm retrieval by vectors and projections. We make a
detailed study of when hyperplanes do norm retrieval. Also, we show that the
families of norm retrievable frames {fi}m
i=1 in Rn are not dense in the family of
m ≤ (2n − 2)-element sets of vectors in Rn for every finite n and the families of
vectors which do norm retrieval in 2 are not dense in the infinite families of vectors
in 2. We also show that if a Riesz basis does norm retrieval in 2 , then it is an
orthogonal sequence. We provide numerous examples to show that our results are
best possible.
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