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Representation of Hilbert space operators by (nJ)-matrices

Published online by Cambridge University Press:  24 October 2008

D. R. Smart
D. R. Smart
Affiliation:
Christ's CollegeCambridge
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Extract

Introduction. Let be the complex separable Hilbert space. We say that the closed linear operator T, with domain dense in. , is represented by the infinite matrix H if T is the operator T˜1(H) defined† by H (with respect to some complete orthonormal set). We define an (nJ)-matrix as a Hermitian matrix H = [hij]i, j ≥ 1 for which hij = 0 when i − j > n and hij ╪ 0 when i − j = n. (Thus a Jacobi matrix is a (1J)-matrix.) If, in addition, hij = 0 when 0 < i − j < n, we call H an (nJ ┴)-matrix.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 53 , Issue 2 , April 1957 , pp. 304 - 311
Copyright
Copyright © Cambridge Philosophical Society 1957

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References

REFERENCES

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