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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

On sums and products of unbounded operators in Hilbert space


Author: M. J. J. Lennon
Journal: Trans. Amer. Math. Soc. 198 (1974), 273-285
MSC: Primary 47A60; Secondary 47A99
DOI: https://doi.org/10.1090/S0002-9947-1974-0350472-5
MathSciNet review: 0350472
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Abstract: The characteristic matrices (in the sense of Stone) of the sum and product of two closed linear operators in Hilbert space are found in terms of the characteristic matrix of each operator. From these, necessary and sufficient conditions for the domain of the sum or product to be dense are found, and a new simple condition for the density of the domain of the sum is proved. The ideas developed are applied to the direct integral decomposition of closed linear operators.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1974-0350472-5
Keywords: Unbounded linear operators, characteristic matrix, direct integral of operators
Article copyright: © Copyright 1974 American Mathematical Society