A polynomial iteration for the spectral family of an operator
1963 ◽
Vol 6
(2)
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pp. 65-69
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Let T be a bounded symmetric operator in a Hilbert space H. According to the spectral theorem, T can be expressed as an integral in terms of its spectral family {Eλ}, each Eλ being a certain projection which is known to be the strong limit of some sequence of polynomials in T. It is a natural question to ask for an explicit sequence of polynomials in T that converges strongly to Eλ. So far as the author knows, no complete solution of this problem has been given even when H has finite dimension, i.e. when T is a finite symmetric matrix. Since a knowledge of the spectral family {Eλ} of a finite symmetric matrix carries with it a knowledge of the eigenvalues and eigenvectors, a solution of the problem may have some practical value.
1963 ◽
Vol 59
(4)
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pp. 727-729
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2020 ◽
Vol 379
(3)
◽
pp. 1077-1112
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2007 ◽
Vol 191
(1)
◽
pp. 79-88
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1979 ◽
Vol 83
(1-2)
◽
pp. 123-132
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